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But the fluid being at rest the pressure downwards on CD, which arises 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 any area CD is equal to the weight of the column of mercury supported in the tube of the barometer, whose base AB is equal to that area.

Wherefore, "The Pressure, &c." Q. E. D.

[COR. 1. By Art. 8. the pressure of a fluid on a horizontal plane immersed in it is 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 column of mercury (of equal section) that 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.]

[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 other fluid quite as well as with mercury. 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 heavier than water (see note p. 57.), it

would take a column of water 13.6 × 30 inches, or 34 feet high, to produce the same effect.]

[COR. 3,

The mercury in the barometer standing at 30 inches, the pressure of the air on a surface whose area is a square inch 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 x 1, or 30, cubic inches of Mercury.-To find how much this pressure amounts to.

The weight of a cubic foot of Water is found to be 1000 ounces avoirdupois ;

the weight of a

cubic foot of Mercury

= 1000 x 13.6 oz. (See page 57. Note.)

[blocks in formation]

[COR. 4. In Chapters I and II the pressure of the air on the surface of the fluid contained in an open vessel has been left out of consideration; or, more properly speaking, the experiments described in those Chapters have been supposed to be made in the exhausted receiver of an air-pump.

From Cor. 2 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 high. In estimating, therefore, the pressure on any surface placed at a given depth below the surface of water, this large additional pressure, (amounting by Cor. 3 to more than

14 lbs. on every square inch of surface), must not be left out of the account.

For suppose two surfaces A and B, each a square inch in area, to be placed horizontally at the respective depths of 2 and 6 feet below the surface of some water at rest. If there be no pressure of air on the horizontal surface of the water, the pressures on A and B will be as 2 6, or as 1 : 3. But if the height of the mercury in the barometer be 30 inches, and the atmosphere is in contact with the surface of the water, then the pressures on A and B will not only be greatly increased, but the ratio they bear to each other will be materially altered; the pressure on A now becoming to that on B as 34 +234 +6, that is as 36 40, or as 9: 10, instead of being, as it was before, as 1

3.]

28. PROP. XIX. To describe the construction of the Common Pump and its Operation.

EF

20

CONSTRUCTION. In the Common Pump two hollow cylinders, AB and BH, having the same axis, are connected together, and at their junction a valve B opening upwards is placed. The higher AB of these D cylinders is called "the Body of the Pump"; in which a piston C, containing a valve opening upwards, plays by means of a rod attached to the end E of a lever EFG whose ful

crum is F. A spout D is placed just above the highest point to which this piston ascends. The lower cylin

C

B

K

Π

der CH, which is called "the Suction Pipe", reaches below the surface H of a well of water.

OPERATION. Let the piston be at B and the suction tube full of air. As C is raised, the pressure of the external air keeps the valve in C closed, and a vacuum being consequently made in the lower part of CB, the air in HB, pressing against the under surface of the valve at B, opens it, and 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, it exercises a less pressure on the surface of the water at H; 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 height K such that the pressure of the air in CK, together with the pressure arising from the column of water KH, produces the same effect on the section of the water in the suction tube at H, as the external air does on an equal area in the surface of the water in the well.

When C has come to 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 and the pressure of the air in CK together with that arising from the fluid column KH, the valve B, being equally pressed on its upper and its under surfaces, will fall down by its own weight. The piston C is then forced down; the air in CB is condensed until its pressure 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, when, on C descending again, it gets above the valve C, and is brought up to the spout at D.

[As the average pressure of the atmosphere will not support a 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 external air in that case not being able 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.]

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

CONSTRUCTION. The Forcing Pump consists of

a Barrel AB in which a solid piston C
works by means of a rod CG; BD is a F
Suction pipe reaching below the surface
D of a well of water; BE a pipe con-
necting BC with a cylinder EF; at B and
E valves are placed, opening upwards.

OPERATION. Suppose the piston C to be at its greatest height, and the pump full of air.

E

G

C

B

H

When C descends, the air in AB is condensed, and its pressure being increased (Prop. XIII.), the valve E is opened, and the air at first in AB is forced into EF.

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