(13) Why does a man learn to swim better in salt water than in fresh?

(14) In Prop. IX., will the result be affected by the greater or less depth, to which the solid is immersed, below the surface of the fluid?

(15) Can the Specific Gravities of fluids, as well as solids, be determined by means of the Hydrostatic Balance? If so, how?

(16) In certain specimens of milk, how would you be able to detect those, if any, which had been adulterated with water?

CHAPTER IV.

ELASTIC FLUIDS.

79. PROP. XII. Air has Weight.

This is proved by the following experiments :

The weight of a vessel from which the air has been exhausted is found to be less than when it was filled with air.

Or, if into a vessel already filled with common air more air be forced, the vessel will then be heavier than it was before.

Also, if a bladder be weighed in a vessel, from which the air has been exhausted, first when the bladder contains no air, and again after air has been forced into it, a greater weight is required to balance the bladder in the latter case.

Whence it is concluded, that "Air has Weight".

The same conclusion seems to follow from the simple consideration, that Air is a fluid, which according to Definition (Art. 58) is a material body, and the property of having weight is considered as necessarily belonging to Matter. See Art. 6.

80. Air is a substance which, besides having weight, possesses the property of self-expansion, so that the matter of which it consists is continually striving to occupy a greater space; and this effort to expand, measured by the pressure required to counteract it, is called the Elastic Force of the air.

81. PROP. XIII. The elastic force of air at a given temperature varies as the density.

This is proved by experiment.

Let ABCD be a glass tube, of uniform bore, b, having the legs AB and CD vertical, the end A of the tube open, and the other end D closed.

A quantity of mercury is poured in at the open end A, so as to confine a quantity of air in the shorter leg CD; the air is then extracted from the longer leg, by means of an instrument for that purpose, and the mercury stands at different heights, E, F, in the two legs. Through E is drawn the horizontal line Ee, meeting the longer leg in e.

Then, the weight of the mercurial column Fe

=

= pressure downwards at e on a surface b, by Prop. IV.,
= pressure upwards at e on a surface b, by Prop. I.,
=pressure upwards at E on a surface b, by Prop. II.,
= pressure by the air in DE on the surface b of mercury
with which it is in contact;

because, the whole being at rest, the pressures upwards and downwards on the same horizontal plane must be equal.

Similarly, when more mercury is poured in, if its surfaces stand at G and H in the two legs, drawing Gg horizontally through G, it follows, that

Weight of the mercurial column Hg= pressure by the air in DG on the portion b of the surface of mercury with which it is in con

tact.

Now, if the lengths ED, Fe, GD, Hg, be measured, it is invariably found, however the quantities of air and of mercury used in the experiment be altered, that (the air retaining the same temperature during the experiment) DE: DG:: Hg: Fe.

A

H

Now, the Elastic Force of the air in DE is measured, as has been shewn, by the weight of the mercurial column

L. C. C.

5

Fe; and that of the air in DG by the weight of the mercurial column Hg; therefore, since the density of the mercury is uniform,

Elastic Force of the air in DG: that of the air in DE

:: volume of mercury in Hg: that of mercury in Fe, :: height Hg: height Fe, (since the bore is uniform,) :: DE: DG, (by what has been shewn,)

:: content of tube DE: that of tube DG.

But the same quantity of air is in DG which was in DE, and its density will be inversely proportional to the space which it occupies*, that is,

Density of the air in DG: that in DE

:: Content of DE: Content of DG,

.. Elastic Force of air in DG: that in DE

:: Density of air in DG : that in DE,

or Elastic Force of air its Density.

82. PROP. XIV. The elastic force of air is increased by an increase of temperature.

This is proved by experiment.

If a bladder partially filled with air be brought near the fire, the enclosed air expands as it becomes heated, and the bladder becomes fully distended. As the enclosed air cools down, the bladder becomes more and more flaccid.

* This has not yet been proved in this Course; but it may be shewn as follows:-Assuming certain standard units of volume and quantity of matter, the Density of a body is most simply defined to be the quantity of matter in a unit of its volume. If, then, D be the Density, V the Volume, Q the quantity of matter, of any body or substance,

and if, while D and V vary, Q remains invariable,

83. DEFS. A VALVE is a kind of door which fits an orifice, so that being pressed by a fluid on one side it opens and allows the fluid to pass through, but keeps the orifice tightly closed, if the fluid press on the other side.

A

C

B

味

Valves are of various forms,—a flap of leather (4) fastened at one edge,—a frustum of a cone (B) made of metal,-a sphere (C),—or a plate of metal (D) with an axis passing perpendicularly through it. By any of these 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 very slight pressures, and so allow fluids of exceedingly small densities to pass under them.

84. PROP. XV. To describe the construction of the common AIR-PUMP, and its operation.

CONSTRUCTION. The AIR-PUMP consists of a glass vessel A, called the Receiver, made to fit a table BC so as to be airtight. A tube DE connects the Receiver with a cylinder EF, called the Barrel. At the bottom of the B Barrel there is a valve E opening

A

D

F

upwards, and a piston F (also furnished with a valve opening upwards) plays within the Barrel.

The instrument is used for pumping the air out of the Receiver A.

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

When the piston is forced down, the air at first in the Barrel is condensed, and its elastic force therefore increased (Prop. XIII.)-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, until the piston reaches the bottom of the Barrel, and the valve F closes by its own weight.

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, until F has reached its highest point. Then the valve E closes by its own weight.

(The figure represents the instrument during the ascent of the piston.)

When the piston descends again, another barrelful of air escapes through the valve F, as before. And so on, until the air in the Receiver becomes so rare, that its pressure is insufficient to overcome the weight of the valve at E.

COR. Hence it appears, that although the air in the Receiver can be very much rarefied, it cannot be wholly exhausted.

85. PROP. XVI. To describe the construction of the CONDENSER, and its operation.

CONSTRUCTION. The CONDENSER is a Barrel AB, furnished with a piston A, which has a valve in it opening downwards; at the bottom of the Barrel there is a fixed valve C, also opening downwards. The neck of the Barrel communicates with a strong air-tight vessel D, called the Receiver.

OPERATION. Suppose the instrument filled with common air, and the piston at its greatest height. On the piston being forced down, the air in the barrel is condensed, and its elastic force being therefore increased (Prop. XIII.), it keeps the valve A closed, opens the valve C, and is driven into the Receiver. (The figure represents the instrument during the descent of the piston.)

Α

B-HE

D

On the piston ascending, the elastic force of the air in the Receiver closes the valve C, and keeps it closed; and there now being no pressure on the under surface of the