above it, the external atmosphere by its pressure keeping the valve H shut; the air in the barrel being thus exhausted, or rarefied, is no longer a counterpoise to that which presses on the surface of the water in the well, this is forced up the pipe, and through the valve K, into the barrel of the pump. Then pushing the piston down again into this water, now in the barrel, its weight shuts the lower valve K, and its resistance forces up the valve of the piston, and enters the upper part of the barrel, above the piston. Then, the bucket being raised, lifts up with it the water which had passed above its valve, and it runs out by the cock L; and taking off the weight below it, the pressure of the external atmosphere on the water in the well again forces it up through the pipe and lower valve close to the piston, all the way as it ascends, thus keeping the barrel always full of water. And thus, by repeating the strokes of the piston, a continued discharge is made at the cock L.

OF THE AIR PUMP.

47. NEARLY on the same principles as the water pump, is the invention of the Air pump, by which the air is drawn out of any vessel, like as water is drawn out by the former. A brass barrel is bored and polished truly cylindri cal, and exactly fitted with a turned piston, so that no air can pass by the sides of it, and furnished with a proper valve opening upwards. Then, by lifting up the piston, the air in the close vessel below it follows the piston, and fills the barrel; and being thus diffused through a larger space than before, when it occupied the vessel or receiver only, but not the barrel, it is made rarer than it was before, in proportion as the capacity of the barrel and receiver together, exceeds the receiver alone. Another stroke of the piston exhausts another barrel of this now rarer air, which again rarefies it in the same proportion as before. And so on, for any number of strokes of the piston, still exhausting in the same geometrical progression, of which the ratio is that which the capacity of the receiver and barrel together exceeds the receiver, till this is exhausted to any proposed degree, or as far as the nature of the machine is capable of performing; which happens when the elasticity of the included air is so far diminished, by rarefying, that it is too feeble to push up the valve of the piston, and

escape.

48. From the nature of this exhausting, in geometrical progression, we may easily find how much the air in the receiver is rarefied by any number of strokes of the piston; or what number of such strokes is necessary, to exhaust the receiver to any given degree. Thus, if the capacity of the receiver and barrel together, be to that of the receiver alone, as c to r, and 1 denote the natural density of the air at first; then,

r

cr:: 1: the density after 1 stroke of the piston,

4n

So, if the barrel be equal to of the receiver; then cr:: 5 : 4; and 5" = 0·8" is = d the density after n turns. And if n be 20, then 0·830 — 0115 is the density of the included 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% times rarefied by the 20 strokes.

49. Or, if it were required to find the number of strokes necessary to rarefy

the air any number of times; because is the proposed density d;

= log. d, and n = of c, and it be required to rarefy the log. 100 1. 5 1. 4

therefore taking the logarithms n× log.
number of strokes required. So, if r be
air 100 times; then d = 55 or ·01; and hence n =
So that in 20 strokes the air will be rarefied 100 times.

--

=203 nearly.

OF THE DIVING BELL, AND CONDENSING MACHINE.

50. 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 upwards, or outwards, in the air-pump, or rarefier, they will both open downwards, or inwards, in the condenser.

51. And on the same principles, namely of the compression 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 downwards; 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.

52. 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 water, 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 CE, 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 CE; but if AB be double of that, or 68 feet, then CD will be CE; and so on. And hence, by knowing the depth AF, to which the vessel is sunk, we can easily find the point D, to which the water will ise 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.

AG

B

F

DE: 34: CE: CE DE,

54 -x: 34:4:4

Ꮖ ;

hence, multiplying the extremes and means, 216

58x+x=136, and the

root is x = 1414 of a foot, or 17 inches nearly; being the height DE to which the water will rise within the tube.

53. 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 nature or shape of the vessel or bell CKL is known.

G

B

F

OF THE BAROMETER.

54. 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 basin of quicksilver, on removing the finger from the orifice, the quicksilver in the tube will descend into the basin, 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 basin. The upper three 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.

So the weight of the quicksilver in the tube, above that in the basin, is at all times equal to the weight or pressure of the column 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 quicksilver 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: for the cubic inch of quicksilver weighs just lb., or nearly a pound, in the mean temperature of 55° of heat. And consequently, when the barometer stands at 30 inches, or 2 feet high, which is the medium or standard height, the whole pressure of the

120

atmosphere is equal to 143 pounds, on every square inch of the base. And so in proportion for other heights.

OF THE THERMOMETER.

55. 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, and its surface rises in the tube; 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 a temperature of just freezing, by immersing the ball in water just freezing,

and

cr 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 between those two points is divided into 180 equal divisions, or degrees; and the like equal degrees are also continued to any extent below the freezing point, and above the boiling point. These 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 Fahrenheit'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 quicksilver in the barometer, that all measures and specific gravities are taken, unless when otherwise mentioned; and in this temperature and pressure, the relative weights, or specific gravities, of air, water, and quicksilver, are as 13 for air, 1000 for water, and 13600 for mercury; and these also are the weights of a cubic foot of each, in avoirdupois ounces, 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.

OF THE MEASUREMENT OF ALTITUDES BY THE

BAROMETER AND THERMOMETER.

56. FROM the principles laid down in the Scholium to prop. 17, concerning the measuring of altitudes by the barometer, and the foregoing descriptions of the barometer and thermometer, we may now collect together the precepts for the practice of such measurements, which are as follow:

First, Observe the height of the barometer at the bottom of any height, or depth, intended to be measured; with the temperature of the quicksilver by means of a thermometer attached to the barometer, and also the temperature of the air in the shade by a detached thermometer.

Second, Let the same thing be done also at the top of the said height or depth, and at the same time, or as near the same time as may be. And let those altitudes of barometer be reduced to the same temperature, if it be thought necessary, by correcting either the one or the other, that is, augment the height