There appears in these experiments sufficient grounds for calling in question the Boylean law; and the writer of this article thought it incumbent on him to repeat them with some precantions, which probably had not been attended to by Mr Sulzer. He was particularly anxious to have the air as free as possible from moisture. For this purpose, having detached the short leg of the syphon, which was 34 inches long, he boiled mercury in it, and filled it with mercury boiling hot. He took a tinplate vessel of sufficient capacity, and put into it a quantity of powdered quicklime just taken from the kiln; and having closed the mouth, he agitated the lime through the air in the vessel, and allowed it to remain there all night. He then emptied the mercury out of the syphon into this vessel, keeping the open end far within it. By this means the short leg of the syphon was filled with very dry air. The other part was now joined, and boiled mercury put into the bend of the syphon; and the experiment was then prosecuted with mercury which had been recently boiled, and was the same with which the barometer had been carefully filled.

The results of the experiments are expressed in the following table.

the differences are even greater than in Mr Sulzer's Elasticity. experiments.

pre

The second table contains the results of experiments 203 made on very damp air in a warm summer's morning. In these it appears that the elasticities are almost cisely proportional to the densities + a small constant quantity, nearly o.11, deviating from this rule chiefly between the densities 1 and 1.5, within which limits we have very nearly D=E1.001. As this air is nearer to the constitution of atmospheric air than the former, this rule may be safely followed in cases where atmospheric air is concerned, as in measuring the depths of pits by the barometer.

The third table shows the compression and elasticity 224 of air strongly impregnated with the vapours of camphire. Here the Boylean law appears pretty exact, or rather the elasticity seems to increase a little faster than the density.

Dr Hooke examined the compression of air by im- 05 mersing a bottle to great depths in the sea, and weighing the water which got into it without any escape of air. But this method was liable to great uncertainty, on account of the unknown temperature of the sea at great depths.

Hitherto we have considered only such air as is not 26 rarer than what we breathe; we must take a very different method for examining the elasticity of rarefied air.

the past

city of n

Let g h (fig. 67.) be a long tube, formed a-top inte Fig. 6. a cup, and of sufficient diameter to receive another Mode of smaller tube af, open at first at both ends. Let the exa outer tube and cup be filled with mercury, which will rise in the inner tube to the same level. Let af now refied at be stopped at a. It contains air of the same density and elasticity with the adjoining atmosphere. Note exactly the space a b which it occupies. Draw it up into the position of fig. 68. and let the mercury stand in it at the Fig. 69. height de, while ce is the height of the mercury in the barometer. It is evident that the column de is in equilibrio between the pressure of the atmosphere and the elasticity of the air included in the space a d. And since the weight of ce would be in equilibrio with the whole pressure of the atmosphere, the weight of c d is equivalent to the elasticity of the included air. While therefore ce is the measure of the elasticity of the surrounding atmosphere, c d will be the measure of the elasticity of the included air; and since the air originally occupied the space a b, and has now expanded into ab a d, we have for the measure of its density. N. B. ce and c d are measured by the perpendicular heights of the columns, but ab and a d must be measured by their solid capacities.

ad

By raising the inner tube still higher, the mercury 207 will also rise higher, and the included air will expand still farther, and we obtain another c d, and another ab and in this manner the relation between the denadi sity and elasticity of rarefied air may be discovered.

208

Experi- eb, and let ec be the height of the mercury in the baments on rometer. Let this apparatus be set under a tubulated Air, receiver on the pump-plate, and let gn be the pump. gage, and mn be equal to ce.

209 Another easy method.

Fig. 70.

210 The most

Then, as has been already shown, cb is the measure of the elasticity of the air in a b, corresponding to the bulk ab. Now let some air be abstracted from the receiver. The elasticity of the remainder will be diminished by its expansion; and therefore the mercury in the tube ae will descend to some point d. For the same reason, the mercury in the gage will rise to some point o, and mo will express the elasticity of the air in the receiver. This would support the mercury in the tube ae at the height er, if the space ar were entirely void of air. Therefore rd is the effect and measure of the elasticity of the included air when it has expanded to the bulk ad; and thus its elasticity, under a variety of other bulks, may be compared with its elasticity when of the bulk ab. When the air has been so far abstracted from the receiver that the mercury in ae descends to e, then mo will be the precise measure of its elasticity. In all these cases it is necessary to compare its bulk ab with its natural bulk, in which its elasticity balances the pressure of the atmosphere. This may be done by laying the tube ae horizontally, and then the air will collapse into its ordinary bulk.

Another easy method may be taken for this examination. Let an apparatus abcdef (fig. 70.) be made, consisting of a horizontal tube ae of even bore, a ball dge of a large diameter, and a swan-neck tube hf. Let the ball and part of the tube geb be filled with mercury, so that the tube may be in the same horizontal plane with the surface de of the mercury in the ball. Then seal up the end a, and connect with an air-pump. When the air is abstracted from the surface de, the air in ab will expand into a larger bulk a c, and the mercury in the pump-gage will rise to some distance below the barometric height. It is evident that this distance, without any farther calculation, will be the measure of the elasticity of the air pressing on the surface de, and therefore of the air in ae.

The most exact of all methods is to suspend in the exact mode receiver of an air-pump a glass vessel, having a very of examin narrow mouth, over a cistern of mercury, and then abing this stract the air till the gage rises to some determined elasticity. height. The difference e between this height and the barometric height determines the elasticity of the air in the receiver and in the suspended vessel. Now lower down that vessel by the slip-wire till its mouth is immersed into the mercury, and admit the air into the receiver; it will press the mercury into the little vessel. Lower it still farther down, till the mercury within it is level with that without; then stop its mouth, take it out and weigh the mercury, and let its weight be w. Subtract this weight from the weight of the mercury, which would completely fill the whole vessel; then the natural bulk of the air will be vw, while its bulk, when of the elasticity e in the rarefied receiver, was the bulk or capacity w of the vessel. Its density therefore, corresponding to this elasticity e, was And thus may the relation between the density and elasticity in all cases be obtained..

VW

w

A great variety of experiments to this purpose have been made, with different degrees of attention, accord

211

made to

this

pose..

ing to the interest which the philosophers had in the Boylean result. Those made by M. de Luc, General Roy, Mr Law. Trembley, and Sir George Shuckburgh, are by far the most accurate; but they are all confined to very Various exmoderate rarefactions. The general result has been, that periments the elasticity of rarefied air is very nearly proportional have been to its density. We cannot say with confidence that any regular deviation from this law has been observed, there purbeing as many observations on one side as on the other; but we think that it is not unworthy the attention of philosophers to determine it with precision in the cases of extreme rarefaction, where the irregularities are most remarkable. The great source of error is a certain adhesive sluggishness of the mercury when the impelling forces are very small; and other fluids can hardly be used, because they either smear the inside of the tube and diminish its capacity, or they are converted into vapour, which alters the law of elasticity.

212

be assumed.

Let us, upon the whole, assume the Boylean law, viz. The Boylethat the elasticity of the air is proportional to its density, an law may. The law deviates not in any sensible degree from the in general truth in those cases which are of the greatest practical" importance, that is, when the density does not much exceed or fall short of that of ordinary air.

213

Let us now see what information this gives us with Investigarespect to the action of the particles on each other. tion of the The investigation is extremely easy. We have seen action of the partithat a force eight times greater than the pressure of cles on the atmosphere will compress common air into the each other. eighth part of its common bulk, and give it eight times its common density and in this case we know, that the particles are at half their former distance, and that the number which are now acting on the surface of the piston employed to compress them is quadruple of the number which act on it when it is of the common density. Therefore, when this eightfold compressing force is distributed over a fourfold number of particles, the portion of it which acts on each is double. In like manner, when a compressing force 27 is employed, the air is compressed into of its former bulk, the particles are at of their former distance, and the force is distributed among 9 times the number of particles ; the force on each is therefore 3. In short, let be the distance of the particles, the number of them in any given vessel, and therefore the density will be as x3, and the number pressing by their elasticity on its whole internal surface will be as . Experiment shows, that the compressing force is as a3, which being distributed over the number as x, will give the force on each as r. Now this force is in immediate equilibrium with the elasticity of the particle immediately contiguous to the compressing surface. This elasticity is therefore as x: and it follows from the nature of perfect fluidity, that the particle adjoining to the compressing surface presses with an equal force on its adjoining particles on every side. Hence we must conclude, that the corpuscularrepulsions exerted by the adjoining particles are inverse-ly as their distances from each other, or that the adjoin-ing particles tend to recede from each other with forces Sir Isaac inversely proportional to their distances.

214

Newton

first who

Sir Isaac Newton was the first who reasoned in this was the manner from the phenomena. Indeed he was the first reasoned who had the patience to reflect on the phenomena. with properly any precision. His discoveries in gravitation naturally on this sube

gave jeet.

Law

Boylean gave his thoughts this turn, and he very early hinted his suspicions that all the characteristic phenomena of tangible matter were produced by forces which were exerted by the particles at small and insensible distances: And he considers the phenomena of air as affording an excellent example of this investigation, and deduces from them the law which we have now demonstrated; and says, that air consists of particles which avoid the adjoining particles with forces inversely proportional to their distances from each other. From this he deduces (in the 2d book of his Principles) several beautiful propositions, determining the mechanical constitution of the atmosphere.

215 Limits the

action to adjoining particles.

216

217

But it must be noticed that he limits this action to the adjoining particles: and this is a remark of immense consequence, though not attended to by the numerous experimenters who adopt the law.

24

-

100

It is plain that the particles are supposed to act at a distance, and that this distance is variable, and that the forces diminish as the distances increase. A very ordinary air-pump will rarefy the air 125 times. The distance of the particles is now 5 times greater than before; and yet they still repel each other: for air of this density will still support the mercury in a syphon-gage at the height of 0.24, or of an inch; and a better pump will allow this air to expand twice as much, and still leave it elastic. Thus we see that whatever is the distance of the particles of common air, they can act five times farther off. The question comes now to be, Whether, in the state of common air, they really do act five times farther than the distance of the adjoining particles? While the particle a acts on the particle with the force 5, does it also act on the particle c with the force 2.5, on the particle d with the force 1.667, on the particle e with the force 1.25, on the particle f with the force I, on the particle g with the force 0.8333, &c.? Sir Isaac Newton shows in the plainest manner, that this is by no means the case; for if this were the case, be makes it appear that the sensible phenomena of condensation would be totally different from what we ob

serve.

The force necessary for a quadruple condensation would be eight times greater, and for a nonuple condensation the force must be 27 times greater. Two spheres filled with condensed air must repel each other, and two spheres containing air that is rarer than the surrounding air must attract each other, &c. &c. All this will appear very clearly, by applying to air the reasoning which Sir Isaac Newton has employed in deducing the sensible law of mutual tendency of two spheres, which consist of particles attracting each other with forces proportional to the square of the distance inversely.

If we could suppose that the particles of air repelled each other with invariable forces at all distances within some small and insensible limit, this would produce a compressibility and elasticity similar to what we observe. For if we consider a row of particles, within this limit, as compressed by an external force applied to the two extremities, the action of the whole row on the extreme points would be proportional to the number of particles, that is, to their distance inversely and to their density: and a number of such parcels, ranged in a straight line, would constitute a row of any sensible magnitude having the

same law of compression. But this law of corpuscular Height force is unlike every thing we observe in nature, and to the Atme the last degree improbable. sphere.

We must therefore continue the limitation of this mu tual repulsion of the particles of air, and be contented for the present with having established it as an experimental fact, that the adjoining particles of air are kept asunder by forces inversely proportional to their distan ces or perhaps it is better to abide by the sensible law that the density of air is proportional to the compressing force. This law is abundantly sufficient for explaining all the subordinate phenomena, and for giving us a complete knowledge of the mechanical constitution of our atmosphere.

218

219

ted from

And in the first place, this view of the compressi-The height bility of the air must give us a very different notion of of the ar the height of the atmosphere from what we deduced on investiga a former occasion from our experiments. It is found, considering that when the air is of the temperature 32° of Fahits compres renheit's thermometer, and the mercury in the barome-sibility, &c. ter stands at 30 inches, it will descend one-tenth of an inch if we take it to a place 87 feet higher. Therefore, if the air were equally dense and heavy throughout, the height of the atmosphere would be 30X10X 87 feet, or 5 miles and 100 yards. But the loose reasoning adduced on that occasion was enough to show us that it must be much higher; because every stratum as we ascend must be successively rarer as it is less compressed by incumbent weight. Not knowing to what degree air expanded when the compression was diminished, we could not tell the successive diminutions of density and consequent augmentation of bulk and height; we could only say, that several atmospheric appearances indicated a much greater height. Clouds have been seen much higher; but the phenomenon of the twilight is the most convincing proof of this. There is no doubt that the visibility of the sky or air is owing to its want of perfect transparency, each particle (whether of matter purely aerial or heterogeneous) reflecting a little light.

2:0

Let b (fig. 71.) be the last particle of illuminated air Fig. 71, wihch can be seen in the horizon by a spectator at A. This must be illuminated by a ray SD 6, touching the earth's surface at some point D. Now it is a known fact, that the degree of illumination called twilight is perceived when the sun is 18° below the horizon of the spectator, that is, when the angle EbS or ACD is 18 degrees; therefore b C is the secant of 9 degrees (it is less, viz. about 8 degrees, on account of refraction). We know the earth's radius to be about 3970 miles: hence we conclude 6 B to be about 45 miles; nay, a very sensible illumination is perceptible much farther from the sun's place than this, perhaps twice as far, and air is sufficiently dense for reflecting a sensible light at the height of nearly 200 miles.

227

fixes no li

mit to the

air's expa

We have now seen that air is prodigiously expansible. Experiment None of our experiments have distinctly shown us any! limit. But it does not follow that it is expansible without end; nor is this at all likely. It is much more sibility. probable that there is a certain distance of the parts in which they no longer repel each other; and this would be the distance at which they would arrange themselves if they were not heavy. But at the very summit of the atmosphere they will be a very small matter nearer to each other, on account of their gravitation to the earth.

Till