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as c to r, and 1 denote the natural density of the air at first :

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So, if the barrel be equal to of the receiver; then c; r

5: 4; and


0.80 is ⇒ d the density after n turns. And if ʼn be 20, then 0.8200115 is the density of the included n air after 20 strokes of the piston; which being the 86, part of 1, or the first density, it follows that the air is 86-7 times rarefied by the 20 strokes.

384. Or, if it were required to find the number of strokes necessary to rarefy the air any number of times; because 19 is the proposed density d; therefore, taking the loga

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log. d.
1. r-1. c'
of c, and it be required to

the number of

rarify the air 100 times then d=。 or 0·1: and hence

log. 100

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1.5 1. 5


203 nearly. So that in 203 strokes the air will be rarefied 100 times.


385. On the same principles too depend the operations and effect of the Condensing Engine, by which air may be condensed to any degree instead of rarefied as in the air-pump. And, like as the air-pump rarefies the air, by extracting always one barrel of air after another; so by this other machine, the air is condensed, by throwing in or adding always one barrel of air after another; which it is evident may be done by only turning the valves of the piston and barrel, that is, making them to open the contrary way, and working the piston in the same manner; so that as they both open upward or outward in



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the air-pump or rarefier, they will both open downward or
inward in the condenser.

386. And on the same principles, namely, of the compres
sion and elasticity of the air, depends the use of the Diving
Bell, which is a large vessel, in which a person descends to
the bottom of the sea, the open end of the vessel being down-
ward; only in this case the air is not condensed by forcing
more of it into the same space, as in the condensing engine;
but by compressing the same quantity of air into a less space
in the bell, by increasing always the force which compresses it.

387. If a vessel of any sort be inverted into water, and pushed or let down to any depth in it; then by the pressure, of the water some of it will ascend into the vessel, but not so high as the water without, and will compress the air into less. space, according to the difference between the heights of the internal and external water; and the density and elastic force of the air will be increased in the same proportion, as its space in the vessel is diminished.

So, if the tube CE be inverted, and pushed down into wa-
ter, till the external water exceed the internal, by the height
AB, and the air of the tube be reduced to the space CD; then
that air is pressed both by a column of
water of the height AB, and by the whole
atmosphere, which presses on the upper
surface of the water; consequently the
space CD is to the whole space ca, as the
weight of the atmosphere, is to the weights
both of the atmosphere and the column
of water AB.
So that if AB be about 34
feet, which is equal to the force of the
atmosphere, then CD will be equal to ICE;
but if AB be double of that, or 68 feet,
then CD will be ce; and so on. And hence, by knowing the
depth ar, to which the vessel is sunk, we can easily find the
point D, to which the water will rise within it at any time. For
let the weight of the atmosphere at that time be equal to that
of 34 feet of water; also, let the depth AF be 20 feet, and
the length of the tube CE 4 feet: then putting the height of
the internal water DE=x,


it is 34+AB : 34 :: ce : CD,


that is 344AF-DE : 34 :: CE : CE-DE,

or 54-x: 34:4:4

hence, multiplying extremes and means, 216-58x+x2=136,
and the root is x2 very nearly 1414 of a foot, or 17
inches nearly; being the height DE to which the water will
rise within the tube.

388. But

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388. But if the vessel be not equally wide throughout, but of any other shape, as of a bell-like form, such as is used in diving; then the altitudes will not observe the proportion above, but the spaces or bulks only will respect that proportion, namely, 34+AB: 34:: capacity CKL capacity CHI, if it be common or fresh water; and 33+ AB: 33:: capacity CKL : capacity CHI, if it be sea-water. From

which proportion, the height DE may be found, when the na ture or shape of the vessel or bell câ, is known,

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389. THE BAROMETER is an instrument for measuring the pressure of the atmosphere, and elasticity of the air, at any time. It is commonly made of a glass tube, of near 3 feet long, close at one end, and filled with mercury. When the tube is full, by stopping the open end with the finger, then inverting the tube, and immersing that end with the finger into a bason of quicksilver, on removing the finger from the orifice, the fluid in the tube will descend into the bason, till what remains in the tube be, of the same weight with a column of the atmosphere, which is commonly between 28 and 31 inches of quicksilver; and leaving an entire vacuum in the upper end of the tube above the mercury. For, as the upper end of the tube is quite void of air, there is no pressure downwards but from the column of quicksilver, and therefore that will be an exact balance to the counter pressure of the whole column of atmosphere, acting on the orifice of the tube by the quicksilver in the bason. The upper 3 inches of the tube, namely, from 28 to 31 inches, have a scale attached to them, divided into inches, tenths, and hundredths, for measuring the length of the column at all times, by observing which division of the scale the top of the quicksilver is opposite to; as it ascends and descends within these limits according to the state of the atmosphere,

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So that the weight of the quick-
silver in the tube, above that in
the bason, is at all times equal to
the weight or pressure of the co-
lumn of atmosphere above it, and
of the same base with the tube
and hence the weight of it may
at all times be computed; being
nearly at the rate of half a pound
avoirdupois for every inch of quick-
silver in the tube, on every square
inch of base; or more exactly it
is of a pound on the square
inch, for every inch in the altitude
of the quicksilver weighs just
or nearly a pound, in the mean
temperature of 55° of heat. And
consequently, when the barometer
stands at 30 inches, or 21 feet high,
which is nearly the medium or
standard height, the whole pressure
of the atmosphere is equal to 143





pounds, on every square inch of the base; and so in proportion for other heights.



390. THE THERMOMETER is an instrument for measuring the temperature of the air, as to heat and cold.

It is found by experience, that all bodies expand by heat, and contract by cold; and hence the degrees of expansion become the measure of the degrees of heat. Fluids are more convenient for this purpose than solids; and quicksilver is now most commonly used for it. A very fine glass tube, having a pretty large hollow ball at the bottom, is filled about half way up with quicksilver: the whole being then heated very hot till the quicksilver rise quite to the top, the top is then hermetically sealed, so as perfectly to exclude all communication with the outward air. Then, in cooling, the quicksilver contracts, and consequently its surface descends in the tube, till it come to a certain point, correspondent to the temperature or heat of the air. And when the weather becomes warmer, the quicksilver expands, VOL. II.




and its surface rises in the tube; and
again contracts and descends when the
weather becomes cooler. So that, by
placing a scale of any divisions against
the side of the tube, it will show the
degrees of heat by the expansion and
contraction of the quicksilver in the
tube; observing at what division of the
scale the top of the quicksilver stands.
And the method of preparing the scale,
as used in England, is thus :-Bring the
thermometer into the temperature of
freezing, by immersing the ball in water
just freezing, or in ice just thawing, and
mark the scale where the mercury then
stands, for the point of freezing. Next,
immerge it in boiling water; and the
quicksilver will rise to a certain height
in the tube; which mark also on the
scale for the boiling point, or the heat
of boiling water. Then the distance be-
tween these two points, is divided into
180 equal divisions, or degrees; and the

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like equal degrees are also continued to any extent below the
freezing point, and above the boiling point. The divisions.
are then numbered as follows; namely at the freezing point
is set the number 32, and consequently 212 at the boiling
point; and all the other numbers in their order.

This division of the scale is commonly called Fabrenheit's.
According to this division, 55 is at the mean temperature of
the air in this country; and it is in this temperature, and in
an atmosphere which sustains a column of 30 inches of quick-
silver in the barometer, that all measures and specific gravities
are taken, unless when otherwise mentioned; and in this tem-
perature and pressure the relative weights, or specific gravi-
ties of air, water and quicksilver, are as

12 for air 1000 for water,

and these also are the weights of a cubic foot of each, in avoirdupois ounces, 13600 for mercury; in that state of the barometer and thermometer. For other states of the thermometer, each of these bodies expands or contracts according to the following rate, with each degree of heat, viz.

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