The condensation therefore is never nearly equal to what is here determined.

It is accurately enough measured by a gage fitted to the instrument. A glass tube GH of a cylindric bore, and close at the end, is screwed into the side of the cap on the mouth of the vessel E. A small drop of mercury is taken into this tube by warming it a little in the hand, which expands the contained air, so that when the open end is dipped into mercury, and the whole allowed to cool, the mercury advances a little into the tube. The tube is furnished with a scale divided into small equal parts, numbered from the close end of the tube. Since this tube communicates with the vessel, it is evident that the condensation will force the mercury along the tube, acting like a piston on the air beyond it, and the air in the tube and vessel will always be of one density. Suppose the number at which the drop stands before the condensation is made to be c, and that it stands at d when the condensation has attained the degree required, the density of the air in the remote end of the gage, and consequently in the vessel, will be \( \frac{c}{d} \).

Sometimes there is used any bit of tube close at one end, having a drop of mercury in it, simply laid into the vessel E, and furnished with a scale; but this can only be used with glass vessels, and these are with difficulty made strong enough to resist the pressure arising from great condensation. In such experiments metallic vessels are generally used, fitted with a variety of apparatus for different experiments.

It must be observed in this place, that very great condensations require great force, and therefore small syringes, for great Syringes It is therefore convenient to have them of various sizes, and condensations require great force, and therefore small syringes, for great to begin with those of a larger diameter, which operate more quickly; and when the condensation becomes fatiguing, to change the syringe for a smaller.

For this reason, and in general to make the condensing apparatus more convenient, it is proper to have a stop-cock interposed between the syringe and the vessel, or, as it is usually called, the receiver. This consists of a brass pipe, which has a well-ground cock in its middle, and has a hollow screw at one end, which receives the nozzle screw of the syringe, and a solid screw at the other end, which fits the screw of the receiver. (See fig. 3.)

By these gages, or contrivances similar to them, we have been able to ascertain very great degrees of condensation in the coarse of some experiments. Dr. Hales found, that condensation, &c., when dry wood was put into a strong vessel, which it almost filled, and the remainder was filled with water, the swelling of the wood, occasioned by its imbibition of water, condensed the air of his gage into the thousandth of its original bulk. He found that pease, treated in the same way, generated elastic air, which, pressing on the air in the gage, condensed it into the fifteen-hundredth part of its bulk. This is the greatest condensation that has been ascertained with precision, although in other experiments it has certainly been carried much farther; but the precise degree could not be ascertained.

Another important observation is, that in every state of Some opis density in which we find it, it retains its perfect fluidity, ions respect transmitting all pressures which are applied to it with undiminished force, as appears by the equality constantly observed between the opposing columns of water or other fluid by which it is compressed, and by the facility with which all motions are performed in it in the most compressed states in which we can make observations of this kind. This fact is totally incompatible with the opinion of those who ascribe the elasticity of air to the springy ramified structure of its particles, touching each other like so many pieces of sponge or foot-balls. A collection of such particles might indeed be pervaded by solid bodies with considerable ease, if they were merely touching each other, and not subjected to any external pressure. But the moment such pressure is exer- ed, and the assemblage squeezed into a smaller space, each presses on its adjoining particles; they are individually compressed, flattened in their touching surfaces, and before the density is doubled they are squeezed into the form of perfect tubes, and compose a mass, which may indeed propagate pressure from one place to another in an imperfect manner, and with great diminution of its intensity, but will no more be fluid than a mass of soft clay.

We have seen the air is heavy and compressible, and of might now proceed to deduce in order the explanation of the appearances consequent on each of these properties. But, as has been already observed, the elasticity of air modifies the effects of its gravity so remarkably, that they would be imperfectly understood if both qualities were not combined in our consideration of either. At any rate, some farther consequences of its elasticity must be considered, before we understand the means of varying at pleasure the effects of its gravity.

Since air is heavy, the lower strata of a mass of air must support the upper; and, being compressible, they must be proved by condensed by their weight. In this state of compression the elasticity of the lower strata of air acts in opposition to the weight of the incumbent air, and balances it. There is no reason which should make us suppose that its expanding force belongs to it only when in such a state of compression. It is more probable that, if we could free it from this pressure, the air would expand itself into still greater bulk. This is most distinctly seen in the following experiment.

Into the cylindric jar ABCD, (fig. 11,) which Fig. 11., has a small hole in its bottom, and is furnished with an air-tight piston E, put a small flaccid bladder, having its mouth tied tight with a string. Having pushed the piston near to the bottom, and noticed the state of the bladder, stop up the hole in the bottom of the jar with the finger, and draw up the piston, which will require a considerable force. You will observe the bladder swell out, as if air had been blown into it; and it will again collapse on allowing the piston to descend. Nothing can be more unexceptionable than the conclusion from this experiment, that ordinary air is in a state of compression, and that its elasticity is not limited to this state. The bladder being flaccid, shows that the included air is in the same state with the air which surrounds it; and the same must be affirmed of it while it swells but still remains flaccid. We must conclude that the whole air within the vessel expands, and continues to fill it, when its capacity has been enlarged. And since this is observed to go on as long as we give it more room, we conclude, that by such experiments we have not yet given it so much room as it can occupy.

Attempts It was a natural object of curiosity to discover the limits of this expansion; to know what was the natural unconfined bulk of a quantity of air, beyond which it would not expand though all external compressing force were removed. Accordingly philosophers constructed instruments for rarefying the air. The common water-pump had been long familiar, and appeared very proper for this purpose. The most obvious is the following.

Let the barrel of the syringe AB communicate with the vessel V, with a stopcock C between them. Let it communicate with the external air by another orifice D, in any convenient situation, also furnished with a stopcock. Let this syringe have a piston very accurately fitted to it so as to touch the bottom all over when pushed down, and have no vacancy about the sides.

Now, suppose the piston at the bottom, the cock C open, and the cock D shut, draw the piston to the top. The air which filled the vessel V will expand so as to fill both that vessel and the barrel AB; and, as no reason can be given to the contrary, we must suppose that the air will be uniformly diffused through both. Calling V and B the capacity of the vessel and barrel, it is plain that the bulk of the air will now be $V+B$; and since the quantity of matter remains the same, and the density of a fluid is as its quantity of matter directly and its bulk inversely, the density of the expanded air will be $\frac{V}{V+B}$, the density of common air being 1; for $V+B$, $V=1$:

$$\frac{V}{V+B}$$

The piston requires force to raise it, and it is raised in opposition to the pressure of the incumbent atmosphere; for this had formerly been balanced by the elasticity of the common air; and we conclude from the fact, that force is required to raise the piston, that the elasticity of the expanded air is less than that of air in its ordinary state; and an accurate observation of the force necessary to raise it would show how much the elasticity is diminished. When therefore the piston is let go, it will descend as long as the pressure of the atmosphere exceeds the elasticity of the air in the barrel; that is, till the air in the barrel is in a state of ordinary density. To put it further down will require force, because the air must be compressed in the barrel; but if we open the cock D, the air will be expelled through it, and the piston will reach the bottom.

Now shut the discharging cock D, and open the cock C, and draw the piston. The air which occupied the space $V$, with the density $\frac{V}{V+B}$ will now occupy the space $V+B$, if it expands so far. To have its density D, say, As its present bulk $V+B$ is to its former bulk $V$, so its former density $\frac{V}{V+B}$ to its new density; which will therefore be $\frac{V \times V}{V+B \times V+B}$, or $\frac{V}{V+B}$:

$$\frac{V}{V+B}$$

It is evident, that if the air continues to expand, the density of the air in the vessel after the third drawing up of the piston will be $\frac{V}{V+B}$, after the fourth it will be $\frac{V}{V+B}$, and after any number of strokes $n$ will be $\frac{V}{V+B}$. Thus, if the vessel is four times as large as the barrel, the density after the fifth stroke will be $\frac{V}{V+B}$, nearly $\frac{1}{2}$ of its ordinary density.

On the other hand, the number $n$ of strokes necessary for reducing air to the density D is $\log \frac{\log D}{\log V - \log (V+B)}$.

Thus we see that this instrument can never abstract the whole air in consequence of its expansion, but only rarely it can continuously as long as it continues to expand; nay, there is excess of a limit beyond which the rarefaction cannot go. When the piston has reached the bottom, there remains a small space between it and the cock C filled with common air. When the piston is drawn up, this small quantity of air expands, and also a similar quantity in the neck of the other cock; and no air will come out of the receiver V till the expanded air in the barrel is of a smaller density than the air in the receiver. This circumstance evidently directs us to make these two spaces as small as possible, or by some contrivance to fill them up altogether. Perhaps this may be done effectually in the following manner. Let BE represent the bottom of the barrel, and let the circle HKI be the section of the key of the cock, of a large diameter, and place it as near to the barrel as can be. Let this communicate with the barrel by means of a hole FG widening upwards, as the frustum of a hollow obtuse cone. Let the bottom of the piston f h g e be shaped so as to fit the bottom of the barrel and this hole exactly. Let the cock be pierced with two holes. One of them, HI, passes perpendicularly through its axis, and forms the communication between the receiver and barrel. The other hole, KL, has one extremity K on the same circumference with H, so that when the key is turned a fourth part round, K will come into the place of H; but this hole is pierced obliquely into the key, and thus keeps clear of the hole HI. It goes no further than the axis, where it communicates with a hole bored along the axis and terminating at its extremity. This hole forms the communication with the external air, and serves for discharging the air in the barrel.

(A side view of the key is seen in fig. 14.) Fig. 13 shows the position of the cock while the piston is moving upwards, and fig. 14 shows its position while the piston is moving downwards. When the piston has reached the bottom, the conical piece f h g of the piston, which may be of firm leather, fills the hole FHG, and therefore completely expels the air from the barrel. The canal KL of the cock contains air of the common density; but this is turned aside into the position KL (fig. 13), while the piston is still touching the cock. It cannot extend into the barrel during the ascent of the piston. In place of it the perforation HLI comes under the piston, filled with air that had been turned aside with it when the piston was at the top of the barrel, and therefore of the same density with the air of the receiver. It appears therefore that there is no limit to the rarefaction as long as the air will expand.

This instrument is called an Exhausting Syringe. It is more generally made in another form, which is much less expensive, and more convenient in its use. Instead of being furnished with cocks for establishing the communications and shutting them, as is necessary, it has valves like those of the condensing syringe, but opening in the opposite direction from those in fig. 10.

This syringe is evidently more easy in its use, requiring no attention to the cocks to open and shut them at the proper times. On this account this construction of an exhausting syringe is much more generally used.

But it is greatly inferior to the syringe with cocks, with respect to its power of rarefaction. It is evident that no air will come out of the receiver unless its elasticity exceed that of the air in the barrel by a difference able to lift up the valve fig. 10. A piece of waxed silk tied across this hole can hardly be made tight and certain of clapping to the hole without some small straining, which must therefore be overcome. It must be very gentle indeed not to require a force equal to the weight of two inches of water, and this is equal to about the 200th part of the whole elasticity of the ordinary air; and therefore this syringe, for this reason alone, cannot rarefy air above 200 times, even though air were capable of an indefinite expansion. In like manner the valve in the piston cannot be raised without a similar Air-pump prevalence of the elasticity of the air in the barrel above the weight of the atmosphere. These causes united, make it difficult to rarefy the air more than 100 times, and very few such syringes will rarefy it more than 50 times; whereas the syringe with cocks, when new and in good order, will rarefy it 1000 times.

But, on the other hand, syringes with cocks are much more expensive, especially when furnished with apparatus for opening and shutting the cocks. They are more difficult to make equally tight, and (which is the greatest objection) do not remain long in good order. The cocks, by so frequently opening and shutting, grow loose, and allow the air to escape. No method has been found of preventing this. They must be ground tight by means of emery or other cutting powders. Some of these unavoidably stick in the metal, and continue to wear it down. For this reason philosophers, and the makers of philosophical instruments, have turned their chief attention to the improvement of the syringe with valves.

OF THE AIR-PUMP.

An Air-Pump is nothing but an exhausting syringe accommodated to a variety of experiments. It was first invented by Otto Guericke, a gentleman of Magdeburgh in Germany, about the year 1654. We trust that it will not be unacceptable to our readers to see this instrument in its first form, and to trace it through its successive steps to its present state of improvement.

Guericke gave a minute description of all his pneumatic apparatus to Gaspar Schottus, professor of mathematics at Wurtemberg, who immediately published it with the author's consent, with an account of some of his performances, first in 1657, in his Mechanica Hydraulico-pneumatica; and then in his Technica Curiosa, in 1664.

Otto Guericke's air-pump consists of a glass receiver A of a form nearly spherical, fitted up with a brass cap and cock B. The nozzle of the cap was fixed to a syringe DE, also of brass, bent at D into half a right angle. This had a valve at D, opening from the receiver into the syringe, and shutting when pressed in the opposite direction. In the upper side of the syringe there is another valve F, opening from the syringe into the external air, and shutting when pressed inwards. The piston had no valve. The syringe, the cock B, and the joint of the tube, were immersed in a cistern filled with water. From this description, it is easy to understand the operation of the instrument. When the piston was drawn up from the bottom of the syringe, the valve F was kept shut by the pressure of the external air, and the valve D opened by the elasticity of the air in the receiver. When it was pushed down again, the valve D immediately shut by the superior elasticity of the air in the syringe; and when this was sufficiently compressed, it opened the valve F, and was discharged. It was immersed in water, that no air might find its way through the joints or cocks.

It would seem that this machine was not very perfect; for Guericke says, that it took several hours to produce an effusion of a moderate-sized vessel; but he says, that when it was in good order, the rarefaction was so great, that Air-pump. When the cock was opened, and water admitted, it filled the receiver so as sometimes to leave no more than the bulk of a pea filled with air. This is a little surprising; for if the valve F he placed as far from the bottom of the syringe as in Schottus' figure, it would appear that the rarefaction could not be greater than what must arise from the air in DF, expanding till it filled the whole syringe; because, as soon as the piston in its descent passes F, it can discharge no more air, but must compress it between F and the bottom, to be expanded again when the piston is drawn up. It is probable that the piston was not very tight, but that on pressing it down, it allowed the air to pass it; and the water in which the whole was immersed prevented the return of the air when it was drawn up again; and this accounts for the great time necessary for producing the desired rarefaction.

Guericke added a part to the machine, which saved his numerous visitants the trouble of hours' attendance, before they could see the curious experiments with rarefied air. He made a larger copper vessel G (fig. 17.), having a pipe and cock below, which passed through the floor of the chamber into an under apartment, where it was joined to the syringe immersed in the cistern of water, and worked by a lever. The upper part of the vessel terminated in a pipe, furnished with a stopcock H, surrounded with a small brim to hold water for preventing the ingress of air. On the top was another cap I, also filled with water, to protect the junction of the pipes with the receiver K. This great vessel was always kept exhausted, and workmen attended below. When experiments were to be performed in the receiver K, it was set on the top of the great vessel, and the cock H was opened. The air in K immediately diffused itself equally between the two vessels, and was so much more rarefied as the receiver K was smaller than the vessel G. When this rarefaction was not sufficient, the attendants below immediately worked the pump.

Guericke's method of excluding air from all the joints of his apparatus, by immersing these joints in water, is the only method that has to this day been found effectual; and there frequently occur experiments where this exclusion for a long time is absolutely necessary. In such cases it is necessary to construct little cups or cisterns at every joint, and to fill them with water or oil. In a letter to Schottus, 1662–3, he describes very ingenious contrivances for producing complete rarefaction after the elasticity of the remaining air has been so far diminished that it is not able to open the valves. He opens the exhausting valves by a plug, which is pushed in by the hand; and the discharging valve is opened by a small pump placed on its outside, so that it opens into a void instead of opening against the pressure of the atmosphere. These contrivances have been lately added to air-pumps by Haas and Hurter as new inventions.

It must be acknowledged, that the application of the pump or syringe to the exhaustion of air was a very obvious thought on the principle exhibited in fig. 3; and in this way it was also employed by Guericke, who first filled the receiver with water, and then applied the syringe. But this was by no means either his object or his principle. His object was not solely to procure a vessel void of air, but to exhaust the air which was already in it; and his principle Air-pump, was the power which he suspected to be in air of expanding itself into a greater space when the force was removed which he supposed to compress it. He expressly says, that the contrivance occurred to him accidentally when occupied with experiments in the Torricellian tube, in which he found that the air would really expand, and completely fill a much larger space than what it usually occupied, and that he had found no limits to the expansion, evincing this by facts which we shall perfectly understand by and bye. This was a doctrine quite new, and required a philosophical mind to view it in a general and systematic manner; and it must be owned, that his manner of treating the subject is equally remarkable for ingenuity and for modesty.

His doctrine and his machine were soon spread over Europe. It was the age of literary ardour and philosophical curiosity; and it is most pleasant to us, who, standing on the shoulders of our predecessors, can see far around us, to observe the eagerness with which every new, and to us frivolous, experiment was repeated and canvassed.

About this time the foundations of the Royal Society of London were laid. Mr. Boyle, Mr. Wren, Lord Brouncker, Mr. Boyce, Dr. Wallis, and others, held meetings at Oxford, in which were received accounts of whatever was doing in the study of nature; and many experiments were exhibited. The researches of Galileo, Toricelli, and Pascal, concerning the pressure of the air, greatly engaged their attention, and many additions were made to their discoveries. Mr. Boyle, the most ardent and successful studier of nature, had the principal share in these improvements, his inquisitive mind being aided by an opulent fortune. In a letter to his nephew Lord Dungarvon, he says that he had made many attempts to see the appearances exhibited by bodies freed from the pressure of the air. He had made Toricellian tubes, having a small vessel a-top, into which he put some bodies before filling the tubes with mercury; so that when the tube was set upright, and the mercury run out, the bodies were in vacuo. He had also abstracted the water from a vessel by a small pump, by means of its weight, in the manner shewn in fig. 3, having previously put bodies into the vessel along with the water. But all these ways were very troublesome and imperfect. He was delighted when he learned from Schottus first publication, that Guericke had effected this by the expansive power of the air; and immediately set about constructing a machine from his own ideas, no description of Guericke's being then published.

It consisted of a receiver A, (fig. 18.) furnished with a stopcock B, and syringe CD placed in a vertical position below the receiver. Its valve C was in its bottom, close adjoining to the entry of the pipe of communication; and the hole by which the air issued was farther secured by a plug which could be removed. The piston was moved by a wheel and rack-work. The receiver of Guericke's pump was but ill adapted for any considerable variety of experiments; and accordingly very few were made in it. Mr. Boyle's receiver had a large opening EF, with a strong glass margin. To this was fitted a strong brass cap, pierced with a hole G in its middle, to which was fitted a plug ground into it, and shaped like the key of a cock. The extremity of this key was furnished with a screw, to which could be affixed a hook, or a variety of pieces for supporting what was to be examined in the receiver, or for producing various motions within it, without admitting the air. This was farther guarded against by means of oil poured round the key, where it was retained by the hollow cup-like form of the cover. With all these precautions, however, Mr. Boyle ingeniously confesses, that it was but seldom, and with great difficulty, that he could produce an extreme degree of rarefaction; and it appears by Guericke's letter to Schottus that in this respect the Magdeburgh machine had the advantage. But most of Boyle's very interesting experiments did not require this extreme rarefaction; and the variety of them, and their philosophic importance, compensated for this defect, and soon eclipsed the fame of the inventor to such a degree, that the state of air in the receiver was generally denominated the vacuum Boyleanum, and the air-pump was called machina Boyleana.

Mr. Boyle found, that to make a vessel air-tight, it was sufficient to place a piece of wet or oiled leather on its brim, and to lay a flat plate of metal on this. The pressure of the external air squeezed the two solid bodies so hard together, that the soft leather effectually excluded it. This enabled him to render the whole machine incomparably more convenient for a variety of experiments. He caused the conduit-pipe to terminate in a flat plate which he covered with leather, and on this he set the glass ball or receiver, which had both its upper and lower brim ground flat. He covered the upper orifice in like manner with a piece of oiled leather and a flat plate, having cocks and a variety of other perforations and contrivances suited to his purposes. This he found infinitely more expeditious, and also tighter than the clammy cements which he had formerly used for securing the joints.

He was now assisted by Dr. Hooke, the most ingenious and inventive mechanic that the world has ever seen. This person made a great improvement on the air-pump, by applying two syringes AA (fig. 19), whose pistons P and P' are both worked by one wheel, O pitching in the racks or piston rods R and R', the pistons being thus raised and depressed alternately by turning the winch W backwards and forwards. In the bottom of each of the barrels there is an opening communicating with the receiver or bell glass B, placed on the plate A, (fig. 20). Over these openings valves of oiled silk are so placed as to admit of the passage of the air from the receiver to the syringe or barrel, but to oppose its passage from the barrel to the receiver. Now, suppose either of the pistons to be at the bottom of its barrel, it is obvious, that on drawing it up a vacuum will be found in the lower portion of the barrel, until the air in the receiver, by its elastic force, opening the valve V or V', rushes in, distributing itself equally betwixt the barrel and receiver, but as the pistons are furnished with valves P and P' similar to and opening in the same direction as VV'; on the descent of the piston the air which occupies the space betwixt the piston and bottom of the barrel being prevented from returning to the receiver by the valve V or V', opens the valve in the piston and escapes into the apartment, with the air of which the piston valve communicates. This evidently doubled the expedition of the pump's operation; but it also greatly diminished the labour of pumping; for it must be observed, that the piston P must be drawn up against the pressure of the external air, and when the rarefaction is nearly perfect, this requires a force of nearly fifteen pounds for every inch of the area of the piston. Now when one piston P is at the top of the barrel, the other P' is at the bottom of the barrel, and the air below P' is equally rare with that in the receiver. Therefore the pressure of the external air on the piston P' is nearly equal to that on the piston P. Both, therefore, are acting in opposite directions on the wheel which gave them motion; and the force necessary for raising P is only the difference between the elasticity of the air in the barrel P, and that of the air in the barrel P'. This is very small in the beginning of the stroke, but gradually increases as the piston P' descends, and becomes equal to the whole excess of the air's pressure above the elasticity of the remaining air of the receiver, when the air at P of the natural density begins to open the piston valves. An accurate attention to the circumstances will show us that the force requisite for working the pump is greatest at first, and gradually diminishes as the rarefaction advances; and when this is nearly complete, hardly any more force is required than what is necessary for overcoming the friction of the pistons, except during the discharge of the air at the end of each stroke. This is therefore the form of the air-pump which is most generally used over all Europe; though in the various modifications some traces of national prepossession remain. We shall give a description of Boyle's air-pump as finally improved by Hawkesbee, which, with some small accommodations to particular views, continued for many years the most approved form.

It consists of two brass barrels a a, (fig. 21,) twelve inches high, and two wide. The pistons are raised and depressed by turning the winch b. This is fastened to an axis passing through a strong toothed wheel, which lays hold of the teeth of the racks c c. Then the one is raised while the other is depressed; by which means the valves, which are made of limber bladder, fixed in the upper part of each piston, as well as in the openings into the bottom of the barrels, perform their office of discharging the air from the barrels, and admitting into them the air from the receiver to be afterwards discharged; and when the receiver comes to be pretty well exhausted of its air, the pressure of the atmosphere in the descending piston is nearly so great, that the power required to raise the other is little more than is necessary for overcoming the friction of the piston, which renders this pump preferable to all Air-pump, others, which require more force to work them as the rarefaction of the air in the receiver advances.

The barrels are set in a brass dish ee, about two inches deep, filled with water or oil to prevent the insinuation of air. The barrels are screwed tight down by two nuts, which force the frontispiece down on them, through which the two pillars pass; for the sake of distinctness, these are omitted in this figure, but are shown in fig. 20.

From between the barrels rises a slender brass pipe h h, communicating with each by a perforation in the transverse piece of brass on which they stand. The upper end of this pipe communicates with another perforated piece of brass, which screws on underneath the plate i i, of ten inches diameter, and surrounded with a brass rim to prevent the shedding of water used in some experiments. This piece of brass has three branches. 1st, An horizontal one communicating with the conduit pipe k k. 2d, An upright one, screwed into the middle of the pump plate, and terminating in a small pipe, rising about an inch above it. 3d, A perpendicular one, looking downwards in the continuation of this pipe, and having a hollow screw in its end receiving the brass cap of the gage-pipe l l, which is of glass, thirty-four inches long, and immersed in a glass cistern filled with mercury. This is covered a-top with a cork float, carrying the weight of a light wooden scale divided into inches, which are numbered from the surface of the mercury in the cistern. This scale will therefore rise and fall with the mercury in the cistern, and indicate the true elevation of that in the tube.

There is a stop-cock immediately above the insertion of the gage-pipe, by which its communication may be cut off. There is another at n, by which a communication is opened with the external air, for allowing its readmission; and there is sometimes another immediately within the insertion of the conduit-pipe for cutting off the communication between the receiver and the pump. This is particularly useful when the rarefaction is to be continued long, as there are by these means fewer chances of the insinuation of air by the many joints.

The receivers are made tight by simply setting them on the pump-plate, with a piece of wet or oiled leather between; and the receivers, which are open a-top, have a brass cover set on them in the same manner. In these covers there are various perforations and contrivances for various purposes. The one in fig. 26 has a slip wire passing through a collar of oiled leather, having a hook or a screw in its lower end, for hanging any thing on, or producing a variety of motions.

Sometimes the receivers are set on another plate, which has a pipe screwed into its middle, furnished with a stop-cock and a screw, which fits the middle pipe k. When the rarefaction has been made in it, the cock is shut, and then the whole may be unscrewed from the pump, and removed to any convenient place. This is called a transporter plate.

It only remains to explain the gage l l. In the ordinary state of the air, its elasticity balances the pressure of the incumbent atmosphere. We find this from the force that is necessary to squeeze it into less bulk in opposition to this elasticity. Therefore the elasticity of the air increases with the vicinity of its particles. It is therefore reasonable to expect, that when we allow it to occupy more room, and its particles are further asunder, its elasticity will be diminished though not annihilated; that is, it will no longer balance the whole pressure of the atmosphere, though it may still balance part of it. If therefore an upright pipe have its lower end immersed in a vessel of mercury, and communicate by its upper end with a vessel containing rarefied, therefore less elastic air, we should expect that the pressure of the air will prevail, and force the mercury into the tube, and cause it to rise to such a height that the weight of the mercury, joined to the elasticity of the rarefied air acting on its upper surface, shall be exactly equal to the whole pressure of the atmosphere. The height of the mercury is the exact measure of that part of the whole pressure which is not balanced by the elasticity of the rarefied air, and its deficiency from the height of the mercury in the Torricellian tube is the exact measure of this remaining elasticity.

It is evident, therefore, that the pipe will be a scale of the elasticity of the remaining air, and will indicate in some sort the degree of rarefaction; for there must be some relation between the density of the air and its elasticity; and we have no reason to imagine that they do not increase and diminish together, although we may be ignorant of the law, that is, of the change of elasticity corresponding to a known change of density. This is to be discovered by experiment; and the air-pump itself furnishes us with the best experiments for this purpose. After rarefying till the mercury in the gage has attained half the height of that in the Torricellian tube, shut the communication with the barrels and gage, and admit the water into the receiver. It will go in till all is again in equilibrium with the pressure of the atmosphere; that is, till the air in the receiver has collapsed into its natural bulk. This we can accurately measure, and compare with the whole capacity of the receiver; and thus obtain the precise degree of rarefaction corresponding to half the natural elasticity. We can do the same thing with the elasticity reduced to one-third, one-fourth, &c., and thus discover the whole law.

This gage must be considered as one of the most ingenious and convenient parts of Hawkesbee's pump; and it is well disposed, being in a situation protected against accidents; but it necessarily increases greatly the size of the machine, and cannot be applied to the table-pump represented in fig. 20. When it is wanted here, a small plate is added behind, or between the barrels and receiver; and on this is set a small tubulated (as it is termed) receiver, covering a common weather-glass tube. This receiver being rarefied along with the other, the pressure on the mercury in the cistern arising from the elasticity of the remaining air, is diminished so as to be no longer able to support the mercury at its full height; and it therefore descends till the height at which it stands puts it in equilibrium with the elasticity. In this form, therefore, the height of the mercury is directly a measure of the remaining elasticity; while in the other it measures the remaining unbalanced pressure of the atmosphere. But this gage is extremely cumbersome, and liable to accidents. We are seldom much interested in the rarefaction till it is great; a contracted form of this gage is therefore very useful, and was early used. A syphon ABCD (fig. 22.) each branch of which is about four inches long, close at A and open at D, is filled with boiling mercury till it occupies the branch AB, and a very small part of CD, having its surface at O. This is fixed to a small stand, and fixed into the receiver, along with the things that are to be exhibited in the rarefied air. When the air has been rarefied till its remaining elasticity is not able to support the column BA, the mercury descends in AB, and rises in CD, and the remaining elasticity will always be measured by the elevation of the mercury in AB above that in the leg CD. Could the exhaustion be perfected, the surfaces in both legs would be on a level. Another gage might be put into the same foot, having a small bubble of air at A. This would expand a complete from the beginning of the rarefaction; but our knowledge of the relation between the density and elasticity does not warrant us in using it as a measure of either.

It is enough for our present purpose to observe, that the Air-pump barometer gage is a perfect indication and measure of the performance of an air-pump, and that a pump is, ceteris paribus, so much the more perfect, as it is able to raise the mercury higher in the gage. It is in this way that we discover that none can produce a complete exhaustion, and that their operation is only a very great rarefaction: for none can raise the mercury to that height at which it stands in the Torricellian tube, well purged of air. Few pumps will bring it within one-tenth of an inch. Hawkesbee's, fitted up according to his instructions, will seldom bring it within one-fifth. Pumps with cocks, when constructed according to the principles mentioned when speaking of the exhausting syringe, and new and in fine order, will in favourable circumstances bring it within one-fortieth. None with valves fitted up with wet leather, or when water or volatile fluids are allowed access into any part, will bring it nearer than one-fifth. Nay, a pump of the best kind, and in the finest order, will have its rarefying power reduced to the lowest standard, as measured by this gage, if we put into the receiver the tenth part of a square inch of white sheep-skin, fresh from the shops, or of any substance equally damp. This is a discovery made by means of the improved air-pump, and leads to very extensive and important consequences in general physics, some of which will be treated of under this article; and the observation is made thus early, that our readers may better understand the improvements which have been made on this celebrated machine.

It would require a volume to describe all the changes which have been made on it. An instrument of such multifarious use, and in the hands of curious men, each diving into the secrets of nature in his favourite line, must have received many alterations and real improvements in many particular respects. But these are beside our present purpose; which is to consider it merely as a machine for rarefying elastic or expansive fluids. We must therefore confine ourselves to this view of it; and shall carefully state to our readers every improvement founded on principle, and on pneumatical laws. All who used it perceived the limit set to the rarefaction by the resistance of the valves, and tried to perfect the construction of the cocks. The Abbé Nollet and s'Gravesande, two of the most eminent experimental philosophers in Europe, were the most successful.

Mr. s'Gravesande justly preferred Hooke's plan of a double pump, and contrived an apparatus for turning the cocks by the motion of the pump's handle. This is far from either being simple or easy in working; and occasions great jerks and concussions in the whole machine. This, however, is not necessarily connected with the truly pneumatical improvement. His piston has no valve, and the rod is connected with it by a stirrup D (fig. 23), as in a common pump. The rod has a cylindric part p, which passes through the stirrup, and has a stiff motion in it up and down of about half an inch; being stopped by the shoulder c above and the nut below. The round plate supported by this stirrup has a short square tube n d, which fits tight into the hole of a piece of cork E. The round plate E has a square shank q, which goes into the square tube n d. A piece of thin leather, soaked in oil, is put between the cork and the plate E, and another between the cork and the plate which forms the sole of the stirrup. All these pieces are screwed together to form the piston by the nail e, whose flat head covers the hole n. Suppose, therefore, the piston touching the bottom of the barrel, and the winch turning to raise it again, the friction of the piston on the barrel keeps it in its place, and the rod is drawn up through the stirrup D. Thus the wheel has liberty to turn about an inch; and this is sufficient for turning the cock, so as to cut off the communication with the external air, and to open the communication with the receiver. This being done, and the motion of the winch continued, the piston is raised to the top of the barrel. When the winch is turned in the opposite direction, the piston remains fixed till the cock is turned, so as to shut the communication with the receiver, and open that with the external air.

This is a pretty contrivance, and does not at first appear necessary; because the cocks might be made to turn at the beginning and end of the stroke without it. But this is just possible; and the smallest error of adjustment, or wearing of the apparatus, will cause them to be open at improper times. Besides, the cocks are not turned in an instant, and are improperly open during some very small time; but this contrivance completely obviates the difficulty.

The cock is precisely similar to that formerly described, having one perforation diametrically through it, and another entering at right angles to this, and after reaching the centre, it passes along the axis of the cock, and comes out to the open air.

It is evident, that by this construction of the cock, the ingenious improvement of Dr. Hooke, by which the pressure of the atmosphere on one piston is made to balance, in great part, the pressure on the other, is given up: for, whenever the communication with the air is opened, it rushes in, and immediately balances the pressure on the upper side of the piston in this barrel; so that the whole pressure in the other must be overcome by the person working the pump. Grav- sande, aware of this, put a valve on the orifice of the cock; that is, tied a slip of wet bladder or oiled leather across it; and now the piston is pressed down, as long as the air in the barrel is rarer than the outward air, in the same manner as when the valve is in the piston itself.

This is all that is necessary to be described in Mrs. Grav- sande's air pump. Its performance is highly extolled by him, as far exceeding his former pumps with valves. The same preference was given to it by his successor Muschenbrock. But, while they both prepared the pistons and valves and leathers of the pump, by steeping them in oil, and then in a mixture of water and spirits of wine, we are certain that no just estimate could be made of its performance. For with this preparation it could not bring the gage within one-fifth of an inch of the barometer. We even see other limits to its rarefaction: from its construction, it is plain that a very considerable space is left between the piston and cock, not less than an inch, from which the air is never expelled; and if this be made extremely small, it is plain that the pump must be worked very slow, otherwise there will not be time for the air to diffuse itself from the receiver into the barrel, especially towards the end, when the expelling force, viz. the elasticity of the remaining air, is very small. There is also the same limit to the rarefaction, as in Hooke's or Hawkesbee's pump, opposed by the valve, which will not open till the air below the piston is considerably denser than the external air; and this pump soon lost any advantages it possessed when fresh from the workman's hands, by the cock's growing loose and admitting air. It is surprising that Grav- sande omitted Hawkesbee's security against this, by placing the barrels in a dish filled with oil; which would effectually have prevented this inconvenience.

We must not omit a seemingly paradoxical observation Advantage of s'Gravesande, that in a pump constructed with valves, and of short worked with a determined uniform velocity, the required degree of rarefaction is sooner produced by short barrels than by long ones. It would require too much time to give a general demonstration of this, but it will easily be seen by an example. Suppose the long barrel to have equal capacity with the receiver, then at the end of the first stroke the Hawkesbee's pump maintained its pre-eminence without rival in Britain till about the year 1750, when it engaged the attention of Mr. John Smeaton. He was then a maker of philosophical instruments, and made many attempts to perfect the pumps with coaks, but found, that whatever perfection he could bring them to, he could not enable them to preserve it; and he never would sell one of this construction. He therefore attached himself solely to the valve pumps.

The first thing was to diminish the resistance to the entry of the air from the receiver into the barrels; and this he rendered almost nothing, by enlarging the surface on which this feebly elastic air was to press. Instead of making these valves to open by its pressure on a circle of one-twentieth of an inch in diameter, he made the valve-hole one inch in diameter, enlarging the surface 400 times; and, to prevent this piece of thin leather from being burst by the great pressure on it, when the piston in its descent was approaching the bottom of the barrel, he supported it by a delicate but strong grating, dividing the valve-hole like the section of a honeycomb, as represented in fig. 24; and the ribs of this grating are seen edgewise in fig. 25, at \(a b c\).

The valve was a piece of thin membrane or oiled silk, gently strained over the mouth of the valve-hole, and tied on by a fine silk thread wound round it in the same manner that the narrow slips had been tied on formerly. This done, he cut with a pointed knife the leather round the edge, nearly four quadrantals across, leaving a small tongue between each, as in fig. 24. The strained valve immediately shrinks inwards, as represented by the shaded parts; and the strain by which it is kept down is now greatly diminished, taking place only at the corners. The gratings being reduced nearly to an edge (but not quite, lest they should cut), there is very little pressure to produce adhesion by the clammy oil. Thus it appears, that a very small elasticity of the air in the receiver will be sufficient to raise the valve; and Mr. Smeaton found, that when it was not able to do this at first, when only about \(\frac{1}{8}\) of the natural elasticity, it would do it after keeping the piston up eight or ten seconds, the air having been all the while undermining the valve, and gradually detaching it from the grating.

Unfortunately he could not follow this method with the piston valve. There was not room round the rod for such an expanded valve; and it would have obliged him to have a great space below the valve, from which he could not expel the air by the descent of the piston. His ingenuity hit on a way of increasing the expelling force through the common valve. He inclosed the rod of the piston in a collar of leather D C (fig. 25,) through which it moved freely without allowing any air to get past its sides. For greater security, the collar of leather was contained in a box terminating in a cap filled with oil. As this makes a material change in the principle of construction of the air-pump, and indeed of pneumatic engines in general, and as it has been adopted in all the subsequent attempts to improve them, it merits a particular consideration.

The piston itself consists of two pieces of brass fastened by screws from below. The uppermost, which is of one solid piece with the rod GH (fig. 25), is of a diameter somewhat less than the barrel; so that when they are screwed together, a piece of leather soaked in a mixture of boiled oil and tallow, is put between them; and when the piston is thrust into Air-pump, the barrel from above, the leather comes up around the side of the piston, and fills the barrel, making the piston perfectly air-tight. The lower half of the piston projects upwards into the upper, which has a hollow \(b c e\) to receive it. There is a small hole through the lower half at \(a\) to admit the air; and a hole \(c d\) in the upper half to let it through, and there is a slip of oiled silk strained across the hole \(a\) by way of valve, and there is room enough left at \(b c\) for this valve to rise a little when pressed from below. The rod GH passes through the piece of brass which forms the top of the barrel so as to move freely, but without any sensible shake: this top is formed into a hollow box, consisting of two pieces E C D F and C N O D, which screw together at CD. This box is filled with rings of oiled leather exactly fitted to its diameter, each having a hole in it for the rod to pass through. When the piece E C D F is screwed down, it compresses the leathers; squeezing them to the rod, so that no air can pass between them; and, so secure us against all ingress of air, the upper part is formed into a cup E F, which is kept filled with oil.

The top of the barrel is also pierced with a hole L K, which rises above the flat surface N O, and has a slip of oiled silk tied over it to act as a valve; opening when pressed from below, but shutting when pressed from above.

The communication between the barrel and receiver is made by means of the pipe A B P Q; and there goes from the hole K in the top of the barrel a pipe K R S T, which either communicates with the open air or with the receiver, by means of the cock at its extremity T. The conduit pipe A B P Q has also a cock at Q, by which it is made to communicate either with the receiver or with the open air. These channels of communication are variously conducted and terminated, according to the views of the maker. The sketch in this figure is sufficient for explaining the principle, and is suited to the general form of the pump, as it has been frequently made by Nairne and other artists in London.

Let us now suppose the piston at the top of the barrel, that it applies to it all over, and that the air in the bar of this conical is very much rarefied: In the common pump the piston structure, valve is pressed hard down by the atmosphere, and continues shut till the piston gets far down, condenses the air below it beyond its natural state, and enables it to force up the valves. But here, as soon as the piston quits the top of the barrel, it leaves a void behind it; for no air gets in round the piston rod, and the valve at K is shut by the pressure of the atmosphere. There is nothing now to oppose the elasticity of the air below but the stiffness of the valve \(b c\); and thus the expelling (or more accurately the liberating) force is prodigiously increased.

The superiority of this construction will be best seen by an example. Suppose the stiffness of the valve equal to the weight of 1-10th of an inch of mercury, when the barometer stands at 30 inches, and that the pump-gage stands at 29-9; then, in an ordinary pump, the valve in the piston will not rise till the piston has got within the 300th part of the bottom of the barrel, and it will leave the valve-hole filled with air of the ordinary density. But in this pump the valve will rise as soon as the piston quits the top of the barrel; and when it is quite down, the valve-hole \(a\) will contain only the 300th part of the air which it would have contained in a pump of the ordinary form. Suppose, farther, that the barrel is of equal capacity with the receiver, Air-pump, and that both pumps are so badly constructed, that the space left below the piston is the 300th part of the barrel. In the common pump the piston valve will rise no more, and the rarefaction can be carried no farther, however delicate the barrel valve may be; but in this pump the next stroke will raise the gage to 29-95, and the piston valve will again rise as soon as the piston gets half-way down the barrel.

The limit to the rarefaction by this pump depends chiefly on the space contained in the hole LK, and in the space b c d of the piston. When the piston is brought up to the top, and applied close to it, those spaces remain filled with air of the ordinary density, which will expand as the piston descends, and thus will retard the opening of the piston valve. The rarefaction will stop when the elasticity of this small quantity of air, expanded so as to fill the whole barrel (by the descent of the piston to the bottom), is just equal to the force requisite for opening the piston valve.

Another advantage attending this construction is, that in drawing up the piston, we are not resisted by the whole pressure of the air; because the air is rarefied above this piston as well as below it, and the piston is in precisely the same state of pressure as if connected with another piston in a double pump. The resistance to the ascent of the piston is the excess of the elasticity of the air above it over the elasticity of the air below; this, toward the end of the rarefaction, is very small, while the piston is near the bottom of the barrel, but gradually increases as the piston rises, and reduces the air above it into smaller dimensions, and becomes equal to the pressure of the atmosphere, when the air above the piston is of the common density. If we should raise the piston still farther, we must condense the air above it; but Mr. Smeaton has here made an issue for the air by a small hole in the top of the barrel, covered with a delicate valve. This allows the air to escape, and shuts again as soon as the piston begins to descend, leaving almost a perfect void behind it as before.

This pump has another advantage. It may be changed in a moment from a rarefying to a condensing engine, by simply turning the cocks at Q and T. Whilst T communicates with the open air and Q with the receiver, it is a rarefying engine or air-pump; but when T communicates with the receiver, and Q with the open air, it is a condensing engine.

Fig. 26 represents Mr. Smeaton's air-pump as it was usually made by Smeaton. Upon a solid base or table are set Air-pump, up three pillars F, H, H; the pillar F supports the pump-plate A, and the pillars H, H, support the front or head, containing a brass cog-wheel, which is turned by the handle B, and works in the rack C fastened to the upper end of the piston rod. The whole is still farther steadied by two pieces of brass n and h, which connect the pump-plate with the front, and have perforations communicating between the hole a in the middle of the plate and the barrel, as will be described immediately. DE is the barrel of the pump, firmly fixed to the table by screws through its upper flanch; ef'dc is a slender brass tube screwed to the bottom of the barrel, and to the under side of the horizontal canal n. In this canal there is a cock m, which opens a communication between the barrel and the receiver, when the key is in the position represented here; but when the key is at right angles with this position, this communication is cut off. If that side of the key which is here drawn next to the pump-plate be turned outward, the external air is admitted into the receiver; but if turned inwards, the air is admitted into the barrel.

g h is another slender brass pipe, leading from the discharging valve at g to the horizontal canal h k, to the under side of which it is screwed fast. In this horizontal canal there is a cock n which opens a passage from the barrel to the receiver when the key is in the position here drawn; but opens a passage from the barrel to the external air when the key is turned outwards, and from the receiver to the external air when the key is turned inwards. This communication with the external air is not immediate but through a sort of box i; the use of this box is to receive the oil which is discharged through the top valve g. In order to keep the pump tight, and in working order, it is proper sometimes to pour a table-spoonful of olive oil into the hole a of the pump-plate, and then to work the pump. The oil goes along the conduit e c d f e, gets into the barrel and through the piston-valve, when the piston is pressed to the bottom of the barrel, and is then drawn up, and forced through the discharging valve g along the pipe g h, the horizontal passage h n, and finally into the box i. This box has a small hole in its side near the top, through which the air escapes.

From the upper side of the canal n there arises a slender pipe which bends outward and then turns downwards, and is joined to a small box, which cannot be seen in this view. From the bottom of this box proceeds downwards the gauge-pipe of glass, which enters the cistern of mercury G fixed below.

On the upper side of the other canal there is a small stud, having a short pipe of glass projecting horizontally from it, close by and parallel to the front piece of the pump, and reaching to the other canal. This pipe is close at the farther end, and has a small drop of mercury or oil in it. This serves as a gage in condensing, indicating the degree of condensation by the place of the drop; for this drop is forced along the pipe, condensing the air before it in the same degree that it is condensed in the barrel and receiver.

In constructing this pump, Mr. Smeaton introduced a method of method of joining together the different pipes and other joint pieces, which has great advantages over the usual manner of screwing them together with leather between, and which is now much used in hydraulic and pneumatic engines. We shall explain this to our readers by a description of the manner in which the exhausting gage is joined to the horizontal duct e b.

The piece h i p, in fig. 27, is the same with the little cylinder observable on the upper side of the horizontal canal n, in fig. 26. The upper part h i is formed into an outside screw, to fit the hollow screw of the piece d e e d. The top of this last piece has a hole in its middle, giving an easy passage to the bent tube e b a, so as to slip along it with Air-pump freedom. To the end e of this bent tube is soldered a piece of brass e f g, perforated in continuation of the tube, and having its end ground flat on the top of the piece h i p, and also covered with a slip of thin leather strained across it and pierced with a hole in the middle.

It is plain from this form, that if the surface f g be applied to the top of h i, and the cover d e e d be screwed down on it, it will draw or press them together, so that no air can escape by the joint; and this without turning the whole tube e b a round, as is necessary in the usual way. This method is now adopted for joining together the conducting pipes of the machines for extinguishing fires, an operation which was extremely troublesome before this improvement.

The conduit pipe E e f e (fig. 26), is fastened to the bottom of the barrel, and the discharging pipe g h to its top, in the same manner. But to return to the gage; the bent pipe e b a (fig. 27), enters the box s t near one side, and obliquely, and the gage-pipe q r is inserted through its bottom towards the opposite side. The use of this box is to catch any drops of mercury which may sometimes be dashed up through the gage-pipe by an accidental oscillation. This, by going through the passages of the pump, would corrode them, and would act particularly on the joints, which are generally soldered with tin. When this happens to an air-pump, it must be cleaned with the most scrupulous attention, otherwise it will be quickly destroyed.

This account of Smeaton's pump is sufficient for enabling the reader to understand its operation and to see its superiority. It is reckoned a very fine pump of the ordinary construction which will rarely 200 times, or raise the gage to 29°85, the barometer standing at 30. But Mr. Smeaton found, that his pump, even after long using, raised it to 29°95, which we consider as equivalent to rarefying 600 times. When in fine order, he found no bounds to its rarefaction, frequently raising the gage as high as the barometer; and he thought its performance so perfect, that the barometer-gage was not sufficiently delicate for measuring the rarefaction. He therefore substituted the syphon-gage already described, which he gives some reasons for preferring; but even this he found not sufficiently sensible.

He contrived another, which could be carried to any degree of sensibility. It consisted of a glass body A (fig. 28), of a pear shape, and was therefore called the pear-gage. This had a small projecting orifice at B, and at the other end a tube CD, whose capacity was the hundredth part of the capacity of the whole vessel. This was suspended at the slip-wire of the receiver, and there was set below it a small cup with mercury. When the pump was worked, the air in the pear-gage was rarefied along with the rest. When the rarefaction was brought to the degree intended, the gage was let down till B reached the bottom of the mercury. The external air being now let in, the mercury was raised into the pear, and stood at some height E in the tube CD. The length of this tube being divided into 100 parts, and those numbered from D, it is evident that DE DB will express the degree of rarefaction which had been produced when the gage was immersed into the mercury; or if DC be \( \frac{1}{10} \) of the whole capacity, and be divided into 100 parts by a scale annexed to it, each unit of the scale will be \( \frac{1}{100} \) of the whole.

This was a very ingenious contrivance, and has been the means of making some very curious and important discoveries. By this gage Mr. Smeaton found, that his pump frequently rarefied a thousand, ten thousand, nay, an hundred thousand times. But though he in every instance saw the great superiority of his pump above all others, he frequently found irregularities which he could not explain, and a want of correspondence between the pear and the barometer gages which puzzled him. The pear-gage frequently indicated a prodigious rarefaction, when the barometer-gage would not show more than 600.

These unaccountable phenomena excited the curiosity of philosophers, who by this time were making continual use of the air-pump in their meteorological researches, and much interested in everything connected with the state or constitution of elastic fluids. Mr. Nairne, a most ingenious and accurate maker of philosophical instruments, made many curious experiments in the examination and comparison of Mr. Smeaton's pump with those of the usual construction, attending to every circumstance which could contribute to the inferiority of the common pumps or to their improvement, so as to bring them nearer to this rival machine. This rigorous comparison brought into view several circumstances in the constitution of the atmospheric air, and its relation to other bodies, which are of the most extensive and important influence in the operations of nature. We shall notice at present such only as have a relation to the operation of the air-pump in extracting air from the receiver.

Mr. Nairne found, that when a little water, or even a bit of paper damped with water, was exposed under the receiver of Mr. Smeaton's air-pump, when in the most perfect condition, raising the mercury in the barometer-gage to 29°95, he could not make it rise above 29°8 if Fahrenheit's thermometer indicated the temperature 47°; nor above 29°7 if the thermometer stood at 55°; and that to bring the gage to this height and keep it there, the operation of the pump must be continued for a long time after the water had disappeared or the paper become perfectly dry. He found that a drop of spirits, or paper moistened with spirits, could not in those circumstances allow the mercury in the gage to rise to near that height; and that similar effects followed from admitting any volatile body whatever into the receiver or any part of the apparatus. This showed him at once how improper were the directions which had been given by Guericke, Boyle, Gravande, and others, for fitting up the air-pump for experiment, by soaking the leather in water, covering the joints with water, or in short, admitting water or any volatile body near it.

He therefore took his pumps to pieces, cleared them of all the moisture which he could drive from them by heat, and then leathered them anew with leather soaked in a mixture of olive oil and tallow, from which he had expelled all the water it usually contains, by boiling it till the first frothing was over. When the pumps were fitted up in this manner, he uniformly found that Mr. Smeaton's pump rarefied the gage to 29°95, and the best common pump to 29°87, the first of which he computed to indicate a rarefaction to 600, and the other to 230. But in this state he again found that a piece of damp paper, leather, wood, &c. in the receiver, reduced the performance in the same manner as before.

But the most remarkable phenomenon was, that when he... Air-pump made use of the pear-gage with the pump cleared from all moisture, it indicated the same degree of rarefaction with the barometer-gage; but when he exposed a bit of paper moistened with spirits, and thus reduced the rarefaction of the pump to what he called 50, the barometer-gage standing at 29-4, the pear-gage indicated a rarefaction exceeding 100,000. In short, it was not measurable; and this phenomenon was almost constant. Whenever he exposed any substance susceptible of evaporation, he found the rarefaction indicated by the barometer-gage greatly reduced, whilst that indicated by the pear-gage was prodigiously increased; and both these effects were the more remarkable as the subject was of easier evaporation, or the temperament of the air of the chamber was warmer.

This uniform result suggested the true cause. Water boils at the temperature of 212°; that is, it is then converted into a vapour which is permanently elastic while of that temperature, and its elasticity balances the pressure of the atmosphere. If this pressure be diminished by rarefying the air above it, a low temperature will now allow it to be converted into elastic vapour, and keep it in that state. Water will boil in the receiver of an air-pump at the temperature of 96°, or even under it. Philosophers did not think of examining the state of the vapour in temperatures lower than what produced ebullition. But it now appears, that in much lower heats than this the superficial water is converted into elastic vapour, which continues to exhale from it as long as the water lasts, and, supplying the place of air in the receiver, exerts the same elasticity, and hinders the mercury from rising in the gage in the same manner as so much air of equal elasticity would have done.

When Mr. Nairne was exhibiting these experiments to the Hon. Henry Cavendish in 1770, this gentleman informed him that it appeared from a series of experiments of his father Lord Charles Cavendish, that when water is of the temperature 72°, it is converted into vapour, under any pressure less than three-fourths of an inch of mercury, and at 41° it becomes vapour when the pressure is less than one-fourth of an inch: even mercury evaporates in this manner when all pressure is removed. A dewy appearance is frequently observed covering the inside of the tube of a barometer, where we usually suppose a vacuum. This dew, when viewed through a microscope, appears to be a set of detached globules of mercury, and upon inclining the tube so that the mercury may ascend along it, these globules will be all licked up, and the tube become clear. The dew which lined it was the vapour of the mercury condensed by the side of the tube; and it is never observed but when one side is exposed to a stream of cold air from a window, &c.

To return to the vapour in the air-pump receiver; it must be observed, that as long as the water continues to yield it, we may continue to work the pump; and it will be continually abstracted by the barrels, and discharged in the form of water, because it collapses as soon as exposed to the external pressure. All this while the gage will not indicate any more rarefaction, because the thing immediately indicated by the barometer-gage is diminished elasticity, which does not happen here. When all the water which the temperature of the room can keep elastic has evaporated under a certain pressure, suppose half an inch of mercury, the gage standing at 29-5, the vapour which now fills the receiver expands, and by its diminished elasticity the gage rises, and now some more water which had been attached to bodies by chemical or corpuscular attraction is detached, and a new supply continues to support the gage at a greater height; and this goes on continually till almost all has been abstracted. But there will remain some which no art can take away; for as it passes through the barrels, and gets between the piston and the top, it successively collapses into water during the ascent of the piston, and again expands into vapour when we push the piston down again. Whenever this happens there is an end of the rarefaction.

Whilst this operation is going on, the air comes out along Air-pump with the vapour; but we cannot say in what proportion, for if it were always uniformly mixed with the vapour, it would uniformly diminish rapidly; but this does not appear to be the case together. There is a certain period of rarefaction in which a transient cloudiness is perceived in the receiver. This is watery vapour formed at that degree of rarefaction, mingled with, but not dissolved in or united with, the air, otherwise it would be transparent. A similar cloud will appear if damp air be admitted suddenly into an exhausted receiver. The vapour, which formed an uniform transparent mass with the air, is either suddenly expanded and thus detached from the other ingredient, or is suddenly let go by the air, which expands more than it does. We cannot affirm with probability which of these is the case. Different compositions of air, that is, air loaded with vapours from different substances, exhibit remarkable differences in this respect. But we see from this and other phenomena, which shall be mentioned in their proper places, that the air and vapour are not always intimately united; and therefore will not always be drawn out together by the air-pump. But let them be ever so confusedly blended, we see that the air must come out along with the vapour, and its quantity remaining in the receiver must be prodigiously diminished by this association, probably much more than could be, had the receiver only contained pure air.

Let us now consider what must happen in the pear-gage. As the air and vapour are continually drawn off from the ces of this receiver, the air in the pear expands and goes off with it. We shall suppose that the generated vapour hinders the gage from rising beyond 29-5. During the continued working of the pump, the air in the pear, whose elasticity is 0-5, slowly mixes with the vapour at the mouth of the pear, and the mixture even advances into its inside, so that if the pumping be long enough continued, what is in the pear is nearly of the same composition with what is in the receiver, consisting perhaps of 20 parts of vapour and one part of air, all of the elasticity of 0-5. When the pear is plunged into the mercury, and the external air allowed to get into the receiver, the mercury rises in the pear-gage, and leaves not

$$\frac{1}{60} \text{ but } \frac{1}{60 \times 20} = \frac{1}{1200}$$

of it filled with common air, the vapour having collapsed into an invisible atom of water. Thus the pear-gage will indicate a rarefaction of 1200, while the barometer-gage only showed 50, that is, showed the elasticity of the included substance diminished 60 times. The conclusion to be drawn from these two measures (the one of the rarefaction of air, and the other of the diminution of elasticity) is, that the matter with which the receiver was filled, immediately before the readmission of the air, consisted of one part of incondensible air, and $$\frac{1200}{60}$$, or 20 parts of watery vapour.

The only obscure part of this account is what relates to Difficulty the composition of the matter which filled the pear-gage in account before the admission of the mercury. It is not easy to see how the vapour of the receiver comes in by a narrow mouth while the air is coming out by the same passage. Accordingly it requires a very long time to produce this extreme rarefaction in the pear-gage; and there are great irregularities in any two succeeding experiments, as may be seen by looking at Mr. Nairne's account of them. Some vapours appear to have mixed much more readily with the air than others; and there are some unaccountable cases where

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1 Phil. Trans., vol. lxvii. Air-pump. Vitriolic acid and sulphureous bodies were included, in which the diminution of density indicated by the pear-gage was uniformly less than the diminution of elasticity indicated by the barometer-gage. It is enough for us at present to have established, by unquestionable facts, this production of elastic vapour, and the necessity of attending to it, both in the construction of the air-pump, and in drawing results from experiments exhibited in it.

Mr. Smeaton's pump, when in good order, and perfectly free from all moisture, will in dry weather rarely air about 600 times, raising the barometer-gage to within \( \frac{1}{3} \)th of an inch of a fine barometer. This was a performance so much superior to that of all others, and by means of Mr. Nairne's experiments opened so new a field of observation, that the air-pumps once more became a capital instrument among the experimental philosophers. The causes of its superiority were also so distinct, that artists were immediately excited to a farther improvement of the machine; so that this becomes a new epoch in its history.

There is one imperfection which Mr. Smeaton has not attempted to remove. The discharging valve is still opened against the pressure of the atmosphere. An author of the Swedish academy adds a subsidiary pump to this valve, which exhausts the air from above it, and thus puts it in the situation of the piston valve. We do not find that this improvement has been adopted so as to become general. Indeed the quantity of air which remains in the passage to this valve is so exceedingly little, that it does not seem to merit attention. Supposing the valve hole \( \frac{1}{2} \)th of an inch wide and as deep (and it need not be more), it will not occupy more than \( \frac{1}{2} \)th part of a barrel twelve inches long and two inches wide.

Mr. Smeaton, by his ingenious construction, has greatly diminished, but has not annihilated, the obstructions to the passage of the air from the receiver into the barrel. His success encouraged farther attempts. One of the first and most ingenious was that of Professor Russell of the University of Edinburgh, who, about the year 1770, constructed a pump in which both cocks and valves were avoided.

The piston is solid, as represented in fig. 28, and its rod passes through a collar of leather on the top of the barrel. This collar is divided into three portions by two brass rings \( a, b \), which leave a very small space round the piston rod. The upper ring \( a \) communicates by means of a lateral perforation with the bent tube \( l m n \), which enters the barrel at its middle \( n \). The lower ring \( b \) communicates with the bent tube \( c d \), which communicates with the horizontal passage \( a e \) going to the middle \( e \) of the pump plate. By the way, however, it communicates also with a barometer gage \( p o \), standing in a cistern of mercury \( o \), and covered with a glass tube close at the top. Beyond \( e \), on the opposite circumference of the receiver plate, there is a cock or plug communicating with the atmosphere.

The piston rod is closely embraced by the three collars of leather; but, as already said, has a free space round it in the two brass rings. To produce this pressure of the leathers to the rod, the brass rings which separate them are turned thinner on the inner side, so that their cross section along a diameter would be a taper wedge. In the side of the piston rod are two cavities \( q r, t s \), about one-tenth of an inch wide and deep, and of a length equal to the thickness of the two rings \( a, b \), and the intermediate collar of leathers. These cavities are so placed on the piston-rod, that when the piston is applied to the bottom of the barrel, the cavity \( t s \) in the upper end of the rod has its upper end opposite to the ring \( a \), and its lower end opposite to the ring \( b \), or to the mouth of the pipe \( c d \). Therefore, if there be a void in the barrel, the air from the receiver will come from the pipe \( c d \), into the cavity in the piston-rod, and by it will get past the collar of leather between the rings, and thus will get into the small interstice between the rod and the upper ring, and then into the pipe \( l m n \), and into the empty barrel. When the piston is drawn up, the solid rod immediately shuts up this passage, and the piston drives the air through the discharging valve \( h \). When it has reached the top of the barrel, and is closely applied to it, the cavity \( q r \) is in the situation in which \( t s \) formerly was, and the communication is again opened between the receiver and the empty barrel, and the air is again diffused between them. Pushing down the piston expels the air by the lower discharging pipe and valve \( h i \); and thus the operation may be continued.

This must be acknowledged to be a most simple and ingenious construction, and can neither be called a cock nor a valve. It seems to oppose no obstruction whatever; and it has the superior advantage of rarefying both during the ascent and the descent of the piston, doubling the expedition of the performance, and the operator is not opposed by the pressure of the atmosphere except towards the end of each stroke. The expedition, however, is not so great as one should expect; for nothing is going on while the piston is in motion, and the operator must stop a while at the end of each stroke, that the air may have time to come through this long, narrow, and crooked passage, to fill the barrel. But the chief difficulty which occurred in the execution arose from the clammy oil with which it was necessary to impregnate the collar of leathers. These were always in a state of strong compression, that they might closely grasp the piston rod, and prevent all passage of air during the motion of the piston. Whenever therefore the cavities in the piston rod come into the situations necessary for connecting the receiver and barrel, this oil is squeezed into them, and chokes them up. Hence it always happened that it was some time after the stroke before the air could force its way round the piston rod, carrying with it the clammy oil which choked up the tube \( l m n \); and when the rarefaction had proceeded a certain length, the diminished elasticity of the air was not able to make its way through these obstructions.

Mr. Cavalle\(^1\) has given the description of an air-pump contrived and executed by Messrs Hans and Hurter, instrument makers in London, where these artists revived Guericke's method of opening the barrel-valve during the last strokes of the pump by a force acting from without. We shall insert as much of this description as relates to the distinguishing circumstance of its construction.

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\(^1\) Phil. Trans. vol. lxiii. Air-pump. Fig. 29 represents a section of the bottom of the barrel, where AA is the barrel, and BB the bottom, which has in its middle a hollow cylinder CCFF, projecting about half an inch into the barrel at CC, and extending a good way downwards to FF. The space between this projection and the sides of the barrel is filled up by a brass ring DD, over the top of which is strained a piece of oiled silk EE, which performs the office of a valve, covering the hole CC. But this hole is filled up by a piece of brass, or rather an assemblage of pieces screwed together GG, HH, II. It consists of three projecting fillets or shoulders GG, HH, II, which form two hollows between them, and which are filled with rings of oiled leather OO, PP, firmly screwed together. The extreme fillets GG, II, are of equal diameter with the inside of the cylinder, so as to fill it exactly, and the whole stuffed with oiled leather, slides up and down without allowing any air to pass. The middle fillet HH is not so broad, but thicker. In the upper fillet GG there is formed a shallow dish about \( \frac{1}{8} \) of an inch deep and \( \frac{3}{4} \) wide. This dish is covered with a thin plate, pierced with a grating like Mr. Smeaton's valve plate. There is a perforation VX along the axis of this piece, which has a passage out at one side H, through the middle fillet. Opposite to this passage, and in the side of the cylinder CC, FF, is a hole M, communicating with the conduit pipe MN, which leads to the receiver. Into the lower end of the perforation is screwed the pin KL, whose tail L passes through the cap FF. The tail L is connected with a lever RQ, moveable round the joint Q. This lever is pushed upwards by a spring, and thus the whole piece which we have been describing is kept in contact with the slip of oiled silk or valve EE. This is the usual situation of things.

Now suppose a void formed in the barrel by drawing up the piston; the elasticity of the air in the receiver, in the pipe MN, and in the passage XV, will press on the great surface of the valve exposed through the grating, will raise it, and the pump will perform precisely as Mr. Smeaton's does. But suppose the rarefaction to have been so long continued, that the air is no longer able to raise the valve; this will be seen by the mercury rising no more in the pump-gage. When this is perceived, the operator must press with his foot on the end R of the lever RQ. This draws down the pin KL, and with it the whole hollow plug with its grated top. And thus, instead of raising the valve from its plate, the plate is here drawn down from the valve. The air now gets in without any obstruction whatever, and the rarefaction proceeds as long as the piston rises. When it is at the top of the barrel, the operator takes his foot from the lever, and the spring presses up the plug again and shuts the valve. The piston rod passes through a collar of leather, as in Mr. Smeaton's pump, and the air is finally discharged through an outward valve in the top of the barrel. These parts have nothing peculiar in them.

This is an ingenious contrivance, similar to what was adapted by Guericke himself; and we have no doubt of these pumps performing extremely well if carefully made; and it seems not difficult to keep the plug perfectly air-tight by supplying plenty of oil to the leathers. We cannot say, however, with precision, what may be expected from it, as no account has been given of its effects, besides what Mr. Cavallo published in the Philosophical Transactions for 1783, where he only says, that when it had been long used, it had, in the course of some experiments, rarefied 600 times.

Aiming still at the removing the obstructions to the entry Air-pump, of the air from the receiver into the barrels, Mr. Prince, an American, has constructed a pump in which there is no valve Prince, or cock whatever between them. In this pump the piston rod passes through a collar of leather, and the air is finally discharged through a valve, as in the two last. But we are chiefly to attend, in this place, to the communication between the barrel and the receiver. The barrel widens below into a sort of cistern ABCD, communicating with the receiver by the pipe EF. As soon, therefore, as the piston gets into this wider part, where there is a vacancy all round it, the air of the receiver expands freely through the passage FEE into the barrel, in which the descent of the piston had made a void. When the piston is again drawn up, as soon as it gets into the cylindric part of the barrel, which it exactly fills, it carries up the air before it, and expels it by the top valve; and, that this may be done more completely, this valve opens into a second barrel or air-pump whose piston is rising at the same time, and therefore the valve of communication (which is the discharging valve of the primary pump) opens with the same facility as Mr. Smeaton's piston valve. While the piston is rising, the air in the receiver expands into the barrel; and when the piston descends, the air in the barrel again collapses till the piston gets again into the cistern, when the air passes out, and fills the evacuated barrel, to be expelled by the piston as before.

No distinct account has yet been given of the performance of this pump. We only learn that great inconveniences were experienced from the oscillations of the mercury in the gage. As soon as the piston comes into the cistern, the air from the receiver immediately rushes into the barrel, and the mercury shoots up in the gage, and gets into a state of oscillation. The subsequent rise of the piston will frequently keep time with the second oscillation, and increase it. The descent of the piston produces a downward oscillation, by allowing the air below it to collapse; and by improperly timing the strokes, this oscillation becomes so great as to make the mercury enter the pump. To prevent this, and a greater irregularity of working as a condenser, valves were put in the piston; but as these require force to open them, the addition seemed rather to increase the evil, by rendering the oscillations more simultaneous with the ordinary rate of working.

It appears, however, of very difficult execution. It has many long, slender, and crooked passages, which must be drilled through broad plates of brass, some of them appearing scarcely practicable. It is rare to find plates and other pieces of brass without air-holes, which it would be very difficult to find out and to close; and it must be very difficult to clear it of obstructions; so that it appears rather a suggestion of theory than a thing warranted by its actual performance.

M. Lavoisier, or some of the philosophers who were occupied in concert with him in the investigation of the different species of gas which are disengaged from bodies in the course of chemical operations, contrived an air-pump which has great appearance of simplicity, and, being very different from all others, deserves to be taken notice of.

It consists of two barrels \( l, m \) (fig. 31) with solid pistons \( k, k \). The pump-plate \( ab \) is pierced at its centre \( e \) with a hole which branches towards each of the barrels, as represented by \( cd, ce \). Between the plate and the barrels slides another plate \( h \), pierced in the middle with a branched hole \( f, d, g \), and near the ends with two holes \( h, i, j \), which go from its under Air-pump side to the ends. The holes in these two plates are so adjusted, that when the plate \( h \) is drawn so far towards \( h \) that the hole \( i \) comes within the barrel \( m \), the branch \( df \) of the hole in the middle plate coincides with the branch \( cd \) of the upper plate, and the holes \( e g \) are shut. Thus a communication is established between the barrel \( l \) and the receiver on the pump-plate, and between the barrel \( m \) and the external air. In this situation the barrel \( l \) will exhaust, and \( m \) will discharge. When the piston of \( l \) is at its mouth, and that of \( m \) touches its bottom, the sliding plate is shifted over to the other side, so that \( m \) communicates with the receiver through the passage \( gd \), \( ee \), and \( l \) communicates with the air by the passage \( hh \).

It is evident that this sliding plate performs the office of four cocks in a very beautiful and simple manner, and that if the pistons apply close to the ends of the barrels so as to expel the whole air, the pump will be perfect. It works, indeed, against the whole pressure of the external air. But this may be avoided by putting valves on the holes \( h i \); and these can do no harm because the air remaining in them never gets back into the barrel till the piston be at the farther end, and the exhaustion of that stroke completed. But the best workmen of London think that it will be incomparably more difficult to execute this cock (for it is a cock of an unusual form), in such a manner that it shall be air-tight and yet move with tolerable ease, and that it is much more liable to wearing loose than common cocks. No accurate accounts have been received of its performance. It must be acknowledged to be ingenious, and it may suggest to an intelligent artist a method of combining common conical cocks upon one axis so as to answer the same purposes much more effectually; for which reason we have inserted it here.

The last improvement which we shall mention, is that published by Mr. Cuthbertson. His pump has given such evidences of its perfection, that we can hardly expect or wish for any thing more complete. But we must be allowed to observe, beforehand, that the same construction was invented, and in part executed, before the end of 1779, by Dr. Daniel Rutherford, then professor of botany in the University of Edinburgh, who was at that time engaged in experiments on the production of air during the combustion of bodies in contact with nitre, and who was vastly desirous of procuring a more complete abstraction of pure aerial matter than could be effected by Mr. Smeaton's pump. The compiler of this article had then an opportunity of perusing the Doctor's dissertation on this subject, which was read in the Philosophical Society of Edinburgh. In this dissertation he appears fully apprised of the existence of pure vital air in the nitrous acid, as its chief ingredient, and as the cause of its most remarkable phenomena, and to want but a step to the discoveries which have emboldened the name of M. Lavoisier. He was particularly anxious to obtain apart this distinguishing ingredient in its composition, and, for this purpose, to abstract completely from the vessel in which he subjected it to examination, every particle of elastic matter. The writer of this article proposed to him to cover the bottom of Mr. Smeaton's piston with some clammy matter, which should take hold of the bottom valve, and start it when the piston is drawn up. A few days after, the Doctor showed him a drawing of a pump, having a conical metal valve in the bottom, furnished with a long slender wire, sliding in the inside of the piston-rod with a gentle friction, sufficient for lifting the valve, and secured against all chance of failure by a spring a-top, which took hold of a notch in the inside of the piston-rod about a quarter of an inch from the lower end, so as certainly to lift the valve during the last quarter of an inch of the piston's motion. Being an excellent mechanic, he had executed a valve on this principle, and was fully satisfied with its performance. But having already confirmed his doctrines respecting the nitrous acid by incontrovertible experiments, his wishes to improve the air-pump lost their incitement, and he thought no more of it; and not long after this the ardour of the philosophers of the Teylerian Society at Haerlem and Amsterdam excited the efforts of Mr. Cuthbertson, their instrument maker, to the same purpose, and produced the most perfect air-pump that has yet appeared. We shall give a description of it, and an account of its performance, in the inventor's own words.

Cuthbertson's Air-Pump.—On fig. 32 is a perspective view of Cuthbertson's pump, with its two principal gages screwed into their places. These need not be used together, except in cases where the utmost exactness is required. In common experiments one of them is removed, and a stop-screw put in its place. When the pear-gage is used, a small round plate, on which the receiver may stand, must be first screwed into the hole at \( A \); but this hole is stepped on other occasions with a screw. When all the three gages are used, and the receiver is exhausted, the stop-screw \( B \), at the bottom of the pump, must be unscrewed, to admit the air into the receiver; but when they are not all used, either of the other stop-screws will answer this purpose.

Fig. 33 represents a cross bar for preventing the barrels from being shaken by working the pump or by any accident. Its place in fig. 32 is represented by the dotted lines. Fig. 34 is a section of one of the barrels, with all its internal parts; and figs. 35, 36, 37, and 38, are different parts of the piston, proportioned in size to one another.

In fig. 34 CD represents the barrel, F the collar of leathers, G a hollow cylindrical vessel to contain oil, R is also an oil-vessel to receive the oil which is drawn, along with the air, through the hole a a, when the piston is drawn upwards; and, when this is full, the oil is carried over with the air, along the tube T, into the oil-vessel G; c e is a wire which is driven upwards from the hole a by the passage of the air; and as soon as this has escaped, it falls down again by its own weight, shuts up the hole, and prevents all return of the air into the barrel. At d d are fixed two pieces of brass, to keep the wire c e in a vertical direction, that it may accurately shut the hole. H is a cylindrical wire or rod which carries the piston I, and is made hollow to receive a long wire g g, which opens and shuts the hole L; and on the other end of the wire O is screwed a nut, which, by stopping in the narrowest part of the hole, prevents the wire from being driven up too far. This wire and screw are more clearly seen in figs. 35 and 39; they slide in a collar of leather r, figs. 35 and 38, in the middle piece of the piston. Figs. 37 and 38 are the two main parts which compose the piston, and when the pieces 36 and 39 are added to it the whole is represented by fig. 35. Fig. 38 is a piece of brass of a conical form, with a shoulder at the bottom. A long hollow screw is cut in it, about two-thirds of its length, and the remainder of the hole, in which there is no screw, is of about the same diameter with the screwed part, except a thin plate at the end, which is of a width exactly equal to the thickness of g g, fig. 34. That part of the inside of the conical brass in which no thread is cut, is filled with oiled leathers with holes through which gg can slide stiffly. There is also a male screw with a hole in it, fitted to gg, serving to compress the leathers r. In fig. 37, a a a is the outside of the piston, the inside of which is turned so as exactly to fit the outside of fig. 38; b b are round leathers about 60 in number, c c is a circular piece of brass of the size of the leathers, and d d is a screw serving to compress them. The screw at the end of fig. 35 is made to fit the screw in fig. 38. Now if fig. 39 be pushed into fig. 38, this into fig. 37, and fig. 36 be screwed into the end of fig. 38, these will compose the whole of the piston, as represented in fig. 34. H, in fig. 34, represents the same part as H in fig. 35, and is that to which the rack is fixed. If, therefore, this be drawn upwards, it will cause fig. 38 to shut close into fig. 37, and drive out the air above it; and when it is pushed downwards it will open as far as the shoulder a a will permit, and suffer air to pass through.

AA (fig. 40) is the receiver plate, BB is a long square piece of brass, screwed into the under side of the plate, through which a hole is drilled corresponding to that in the centre of the receiver-plates and with three female screws a, b, c.

The rarefaction of the air in the receiver is effected as follows. Suppose the piston at the bottom of the barrel. The inside of the barrel, from the top of the piston to a, (fig. 34) contains common air. When the rod is drawn up, the outer part of the piston sticks fast in the barrel till the conical part connected with the rod shuts the conical hole, and its shoulder applies close to its bottom. The piston is now shut, and therefore the whole is drawn up by the rack-work, driving the air before it through the hole a e, into the oil-vessel at R, and out into the room by the tube T. The piston will then be at the top of the barrel at a, and the wire gg will stand nearly as represented in the figure just raised from the hole L, and prevented from rising higher by the nut O. During this motion the air will expand in the receiver, and come along the bent tube as into the barrel. Thus the barrel will be filled with air, which, as the piston rises, will be rarefied in proportion as the capacity of the receiver, pipes, and barrel, is to the barrel alone. When the piston is moved down again by the rack-work, it will force the conical part (fig. 38) out of the hollow part (fig. 37) as far as the shoulders a a; fig. 35 will rest on a a (fig. 37) which will then be so far open as to permit the air to pass freely through it, while at the same time the end of gg is forced against the top of the hole, and shuts it, in order to prevent any air from returning into the receiver. Thus the piston, moving downwards, suffers the air to pass out between the sides of figs. 37 and 38; and, when it is at the bottom of the barrel, will have the column of air above it; and, consequently, when drawn upwards it will shut, and drive out this air, and, by opening the hole L at the same time, will give a free passage to more air from the receiver. This process being continued, the air of the receiver will be rarefied as far as its expansive power will permit. For in this machine there are no valves to be forced open by the

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1 The piston and barrel are 1-65 inches in diameter, in proportion to which the scale is drawn. Figures 35, 36, 37, and 38, are however, of double size. elasticity of the air in the receiver, which at last it is unable to effect. There is therefore nothing to prevent the air from expanding to its utmost degree.

It may be suspected here, that as the air must escape through the discharging passage ac, fig. 34, against the pressure of a column of oil and the weight of the wire, there will remain in this passage a quantity of air of considerable density, which will expand again into the barrel during the descent of the piston, and thus put a stop to the progress of rarefaction. This is the case in Mr. Smeaton's pump, and all which have valves in the piston. But it is the peculiar excellency of this pump, that whatever be the density of the air remaining in ac, the rarefaction will still go on. It is worth while to be perfectly convinced of this. Let us suppose that the air contained in ac is \( \frac{1}{10} \)th part of the common air which would fill the barrel, and that the capacity of the barrel is equal to that of the receiver and passages, and that the air in the receiver and barrel is of the same density, the piston being at the bottom of the barrel; the barrel will therefore contain \( \frac{1}{10} \) parts of its natural quantity, and the receiver \( \frac{1}{10} \). Now let the piston be drawn up. No air will be discharged at ac, because it will contain the whole air which was in the barrel, and which has now collapsed into its ordinary bulk. But this does not in the least hinder the air of the receiver from expanding into the barrel, and diffusing itself equally between both. Each will now contain \( \frac{1}{10} \) of their ordinary quantity when the piston is at the top, and ac will contain \( \frac{1}{10} \) as before, or \( \frac{1}{10} \).

Now push down the piston. The hole L is instantly shut, and the air in ac expands into the barrel, and the barrel now contains \( \frac{1}{10} \). When the piston reaches the bottom, there will be \( \frac{1}{10} \) in the barrel. When again drawn up to the top, there will be \( \frac{1}{10} \) discharged, and the receiver will contain \( \frac{1}{10} \); and when the piston reaches the bottom, there will be \( \frac{1}{10} \). At the next stroke the receiver will contain only \( \frac{1}{10} \), &c. &c.

Thus it appears, that notwithstanding the \( \frac{1}{10} \) which always expands back again out of the hole ac into the barrel, the rarity of the air in the receiver will be doubled at every stroke. There is therefore no need of a subsidiary air-pump at c, as in the American air-pump, and in the Swedish attempt to improve Smeaton's.

In using this air-pump no particular directions are necessary, nor is any peculiar care necessary for keeping it in order, except that the oil-vessel G be always kept about half full of oil. When the pump has stood long without being used, it will be proper to draw a table-spoonful of olive-oil through it, by pouring it into the hole in the middle of the receiver-plate when the piston is at the bottom of the barrel. Then by working the piston, the oil will be drawn through all the parts of the pump, and the surplus will be driven through the tube T into the oil-vessel G. Near the top of the piston rod at H, there is a hole which lets some oil into the inside of the rod, which gets at the collar of len-Air-pump, thers rr, and keeps the wire gy air-tight.

When the pump is used for condensation at the same time that it rarifies, or separately, the piece containing the bent tube T must be removed, and fig. 41 put into its place, and fixed by its screws. Fig. 41, as drawn in the plate, is intended for a double-barrelled pump. But for a single barrel only one piece is used, represented by b a a, the double piece being cut off at the dotted line a a. In this piece is a female screw to receive the end of a long brass tube, to which a bladder (if sufficient for the experiment of condensation,) or a glass, properly secured for this purpose, must be screwed. Then the air which is abstracted from the receiver on the pump-plate will be forced into the bladder or glass. But if the pump be double, the apparatus fig. 41 is used, and the long brass tube screwed on at c.

Figs. 42 and 43 represent the two gages, which will be sufficiently explained afterwards. Fig. 42 is screwed into b, or into the screw at the other end c, fig. 40, and fig 43 into the screw a, fig. 40.

If it be used as a single pump, either to rarify or to condense, the screw K, which fastens the rack to the piston rod H, must be taken out. Then turning the winch till H is depressed as low as possible, the machine will be fitted to exhaust as a single pump; and if it be required to condense, the directions formerly given must be observed with regard to the tube T, and fig. 41.

"I took," says Mr. Cuthbertson, "two barometer tubes of an equal bore with that fixed to the pump. These were filled with mercury four times boiled. They were then compared, and stood exactly at the same height. The mercury in one of them was boiled in it four times more, without making any change in their height; they were therefore judged very perfect. One of these was immersed in the cistern of the pump gage, and fastened in a position parallel to it, and a sliding scale of one inch was attached to it. This scale, when the gage is used, must have its upper edge set equal with the surface of the mercury in the boiled tube after exhaustion, and the difference between the height of the mercury in this and in the other barometer tube may be observed to the \( \frac{1}{10} \) of an inch; and being close together, no error arises from their not being exactly vertical, if they are only parallel. This gage will be better understood by inspecting fig. 43.

"I used a second gage, which I shall call a double siphon. (See fig. 42.) This was also prepared with the utmost care. I had a scale for measuring the difference between the height of the columns in the two legs. It was an inch long, and divided as the former, and kept in a truly vertical position by suspending it from a point with

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*An air-pump of this description is by far too delicate to be employed without risk of injury in experiments on condensed air.* Air-pump, a weight hung to it, as represented in the figure. Upon comparing these two gages, I always found them to indicate the same degree of rarefaction. I also used a pear-gage, though the most imperfect of all, in order to repeat the curious experiments of Mr. Nairne and others.

When experiments require the utmost rarefying power of the pump, the receiver must not be placed on leather, either oiled or soaked in water, as is usually done. The pump plate and the edge of the receiver must be ground very flat and true, and this with very fine emery, that no roughness may remain. The plate of the pump must then be wiped very clean and very dry, and the receiver rubbed with a warm cloth till it become electrical. The receiver being now set on the plate, hog's lard, either alone or mixed with a little oil which has been cleared of water by boiling, must be smeared round its outside edge. In this condition the pump will rarefy its utmost, and what still remains in the receiver will be permanent air. Or a little of this composition may be thinly smeared on the pump plate; this will prevent all risk of scratching it with the edge of the receiver. Leather of very uniform thickness, long dried before a fire, and well soaked in this composition, which must be cleared of all water by the first boiling, will answer very well, and is expeditions, when receivers are to be frequently shifted. Other leathers should be at hand soaked in a composition containing a little rosin. This gives it a clamminess which renders it impermeable to air, and is very proper at all joints of the pump, and all apparatus for pneumatic experiments. As it is impossible to render the pear-gage as dry as other parts of the apparatus, there will be generally some variation between this and the other gages.

When it is only intended to show the utmost power of the pump, without intending to ascertain the quality of the residuum, the receiver may be set on wet leather. If, in this condition, the air be rarefied as far as possible, the syphon and barometer gage will indicate a less degree of rarefaction than in the former experiments. But when the air is let in again, the pear gage will point out a rarefaction some thousands of times greater than it did before. If the true quantity of permanent air after exhaustion be required, the pear gage will be nearest the truth; for when the air is rarefied to a certain degree, the moistened leather emits an expansible fluid, which, filling the receiver, forces out the permanent air; and the two first gages indicate a degree of exhaustion which relates to the whole elastic matter remaining in the receiver, viz. to the expansible fluid together with the permanent air; whereas the pear gage points out the degree of exhaustion, with relation to the permanent air alone, which remains in the receiver; for by the pressure of the air admitted into the receiver, the elastic vapour is reduced to its former bulk, which is imperceptible.

Many bodies emit this elastic fluid when the pressure of the air is much diminished; a piece of leather, in its ordinary damp state, about an inch square, or a bit of green or dry wood, will supply this for a great while. When such fluids have been generated in any experiments, the pump must be carefully cleared of them, for they remain not only in the receiver, but in the barrels and passages, and will again expand when the exhaustion has been carried far.

The best method of clearing the pump is to take a very large receiver, and, using every precaution, to exhaust it as far as possible. Then the expansible matter lurking in the barrels and passes will be diffused through the receiver also, or will be carried off along with its air. It will be as much rarer than it was before, as the aggregate capacity of the receiver, barrels and passes is larger than that of the two last.

The performance of the pump may be judged of from Air pump, the four following experiments: The two gages being screwed into their places, and the hole in the receiver-plate shut up the pump was made to exhaust as far as it could. The mercury in the legs of the siphon was only \( \frac{1}{4} \) of an inch out of the level, and that in the boiled barometer-tube \( \frac{1}{2} \) of an inch higher than in the one screwed to the pump. A standard barometer then stood at 30 inches, and therefore the pump rarefied the permanent air 1200 times. This is twice as much as Mr. Nairne found Mr. Smeaton's do in its best state. Mr. Cavallo seems disposed to give a favourable account of Haas and Hurter's pump, and it appears never to have exceeded 600 times. Mr. Cuthbertson has often found the mercury within \( \frac{1}{4} \) of an inch of the level in the syphon-gage, indicating a rarefaction of 3000.

To one end of a glass tube, two inches diameter and thirty inches long, was fitted a brass cap and collar of leather, through which a wire was inserted, reaching about two inches within the tube. This was connected with the conductor of an electric machine. The other end was ground flat and set on the pump plate. When the gages indicated a rarefaction of 300, the light became steady and uniform, of a pale colour, though a little tinged with purple; at 600 the light was of a pale dusky white; when 1200 it disappeared in the middle of the tube, and the tube conducted so well that the prime conductor only gave sparks so faint and short as to be scarcely perceptible. After taking off the tube, and making it as dry as possible, it was again connected with the conductor, which was giving sparks two inches long. When the air in it was rarefied ten times, the sparks were of the same length. Sometimes a pencil of light darted along the tube. When the rarefaction was 20, the spark did not exceed an inch, and light streamed the whole length of the tube. When the rarefaction was 30, the sparks were half an inch, and the light rushed along the tube in great streams. When the rarefaction was 100, the sparks were about \( \frac{1}{2} \) long, and the light filled the tube in an uninterrupted body. When 300, the appearances were as before. When 600, the sparks were \( \frac{1}{8} \), and the light was of a faint white colour in the middle, but tinged with purple toward the ends. When 1200, the light was hardly perceptible in the middle, and was much fainter at the ends than before, but still ruddy. When 1400, which was the most the pump could produce, six inches of the middle of the tube were quite dark, and the ends free of any tinge of red, and the sparks did not exceed \( \frac{1}{8} \) of an inch.

We trust that our readers will not be displeased with the preceding history of the air-pump. The occasional information which it gives will be of great use to every personments of much engaged in pneumatic experiments, and help him in the contrivance and construction of the necessary apparatus. We may be indulged in one remark, that although this noble instrument originated in Germany, all its improvements were made in this kingdom. Both the mechanical and pneumatic principles of Mr. Boyle's construction were extremely different from the German, and, in respect of expedition and convenience, much superior. The double barrel and gage by Hawkesbee were capital improvements, and on principle; and Mr. Smeaton's method of making the piston work in rarefied air made a complete change in the whole process.

Aided by this machine, we can make experiments establishing and illustrating the gravity and elasticity of the air, the air in a much more perspicuous manner than could be done by pump. the spontaneous phenomena of nature. It allows us in the Air-pump first place to show the materiality of air in a very distinct manner. Bodies cannot move about in the atmosphere without displacing it. This requires force; and the resistance of the air always diminishes the velocity of bodies moving in it. A heavy body therefore has the velocity of its fall diminished; and if the quantity of air displaced be very great, the diminution will be very considerable. This is the reason why light bodies, such as feathers, fall very slowly. Their moving force is very small, and can therefore displace a great quantity of air only with a very small velocity. But if the same body be dropped in vacuo, when there is no air to be displaced, it falls with the whole velocity competent to its gravity. Fig. 44 represents an apparatus by which a guinea and a downy feather are dropped at the same instant. If this be done after the air has been pumped out, the guinea and the feather will be observed to reach the bottom at the same instant.

Fig. 45 represents another apparatus for showing the same thing. It consists of two sets of brass vanes put on separate axles, in the manner of windmill sails. One set has their edges placed in the direction of their whirling motion, that is, in a plane to which the axis is perpendicular. The planes of the other set pass through the axis, and they are therefore trimmed so as directly to front the air through which they move. Two springs act upon pins projecting from the axis; and their strength or tensions are so adjusted, that when they are disengaged in vacuo, the two sets continue in motion equally long. If they are disengaged in the air, the vanes which beat the air with their planes will stop long before those which cut it edgewise.

We can now abstract the air most completely from a dry vessel, so as to know the precise weight of the air which filled it. The first experiment we have of this kind, done with accuracy, is that of Dr. Hooke, February 10, 1654, when he found 114 pints of air to weigh 945 grains. One pint of water was $8\frac{3}{4}$ ounces. This gives for the specific gravity of air $\frac{1}{27}$ very nearly.

Since we are thus immersed in a gravitating fluid, it follows that every body preponderates only with the excess of air on its own weight above that of the air which it displaces; the weight for every body loses by this immersion the weight of the immersed displaced air. A cubic foot loses about 521 grains in frosty weather. We see balloons even rise in the air, as a piece of cork rises in water. A mass of water which really contains 850 pounds will load the scale of a balance with 849 only, and will be balanced by about 849$\frac{1}{2}$ pounds of brass. This is evinced by a very pretty experiment, represented in fig. 46. A small beam is suspended within a receiver. To one end of the beam is appended a thin glass or copper ball, close in every part. This is balanced by a small piece of lead hung on the other arm. As the air is pumped out of the receiver, the ball will gradually preponderate, and will regain its equilibrium when the air is re-admitted.

Some philosophers have proposed, and even used, a large globe of light make, suspended at a beam, for a barometer. If its capacity be a cubic foot, 1$\frac{1}{2}$ grains will indicate the

vantages of Mr. Cuthbertson's, with this other in addition, that it is much simpler in its construction. Fig. 1 presents a view of this pump. AA

are the barrels. B the pipe leading from them to C the receiver plate D the barometer gage. E a stop cock for re-admitting the air for attaching a siphon gage, or other piece of apparatus. Fig. 2 is a section of the piston and of the under part of one of the barrels, shewing the whole of the internal construction; A A, e a is the barrel, O N the pistons, G I the piston rod containing the rod r, which slides in the collar of leathers T, and opens the valve v e j; in this respect it is precisely the same as Cuthbertson's, but the maker dispenses with all the apparatus at the top of Cuthbertson's barrels, and has only an oiled silk valve S. in the piston, which is exposed to the atmosphere, as in Hook's pump. The exclusion of the atmosphere from the piston valve, the maker considers an unnecessary expense. From the account previously given of the performance of Cuthbertson's, and of the other pumps described, as well as from his own experience, he is of opinion that the action of the barrel is not interfered with either by the formation of elastic vapour from the oil necessarily present, or from some unknown property of the air itself, long before it has been so much rarefied as to be unable to open the piston valves. His reasons for this opinion is, that the capacity of the barrels of any well-constructed pump is several thousand times greater than the space which exists between the valves, when the piston has reached the bottom of the barrel; in short, it may be limited to the small hole S N. For example, in the pump, the length of the stroke of which is 12 inches, the diameter of the barrels 2½ in., the diameter of the hole S N, ¼ th of an inch, and its length one inch, the capacity of the hole S N is 7500 times less than the capacity of the barrel, and consequently air 7500 times rarer than the atmosphere when filling the whole barrel, will, by the descent of the piston, become of the same density, but as it is known from the performance of Hook's pump, that air $\frac{1}{27}$th part of the density of the atmosphere has sufficient elastic force to open an oil silk valve, it follows that the pump we have supposed, will exhaust 7125 times, but as this degree of exhaustion has never yet been attained, it is evident that some other reason must be assigned for in explanation of this, than the imperfection of the mechanical arrangement. A metallic valve T p, may be placed in the piston instead of the oiled silk one, having a projecting point p to open it, on the piston reaching the bottom of the barrel, and a space OT filled with oil, to prevent the return of the air during the time which elapses betwixt the commencement of the ascent of the piston and the complete shutting of the valve. Air-pump. same change that is indicated by \( \frac{1}{2} \) of an inch of an ordinary barometer. But a vessel of this size will load a balance too much to leave it sufficiently sensible to small changes of density. Besides, it is affected by heat and cold, and would require a very troublesome equation to correct their effects.

It may perhaps be worth while to attend to this in buying and selling precious commodities; such as pearls, diamonds, silk, and some drugs. As they are generally sold by brass or leaden weights, the buyer will have some advantage when the air is heavy and the barometer high. On the other hand, he will have the advantage in buying gold and mercury when the air is light. It is needless to confine this observation to precious commodities, for the advantage is the same in all in proportion to their levity.

There is a case in which this observation is of consequence to the philosopher: we mean the measuring of time by pendulums. As the accelerating force on a pendulum is not its whole weight, but the excess of its weight over that of the displaced air, it follows that a pendulum will vibrate more slowly in the air than in vacuo. A pendulum composed of lead, iron, and brass, may be about 8400 times heavier than the air which it displaces when the barometer is at 30 inches and the thermometer is at 32°, and the accelerating force will be diminished about \( \frac{1}{16} \). This will cause a second pendulum to make about five vibrations less in a day than it would do in vacuo. In order therefore to deduce the accelerative power of gravity from the length of a pendulum vibrating in the air, we must make an allowance of 0°.17, or \( \frac{1}{50} \) of a second per day, for every inch that the barometer stands lower than 30 inches. But we must also note the temperature of the air; because when the air is warm it is less dense when supporting by its elasticity the same weight of atmosphere, and we must know how much its density is diminished by an increase of temperature. The correction is still more complicated; for the change of density affects the resistance of the air, and this affects the time of the vibration, and this by a law that is not yet well ascertained. As far as we can determine from any experiments that have been made, it appears that the change arising from the altered resistance takes off about 2-5ths of the change produced by the altered density, and that a second pendulum makes but three vibrations a-day more in vacuo than in the open air. This is a very unexpected result; but it must be owned that the experiments have neither been numerous nor very nicely made.

The air-pump also allows us to show the effects of the air's pressure in a great number of amusing and instructive phenomena.

When the air is abstracted from the receiver, it is strongly pressed to the pump-plate by the incumbent atmosphere, and it supports this great pressure in consequence of its circular form. Being equally compressed on all sides, there is no place where it should give way rather than another; but if it be thin, and not very round, which is sometimes the case, it will be crushed to pieces. If we take a square thin vial, and apply an exhausting syringe to its mouth, it will not fail being crushed.

As the operation of pumping is something like sucking, many of these phenomena are in common discourse ascribed to suction, a word much abused; and this abuse misleads the mind exceedingly in its contemplation of natural phenomena. Nothing is more usual than to speak of the suction of a syringe, the suction and draught of a chimney, &c. The following experiment puts the true cause of the strong adhesion of the receiver beyond a doubt.

Place a small receiver, or cupping-glass on the pump-plate without covering the central hole, as represented in fig. 47, and cover it with a larger receiver. Exhaust the air from it; then admit it as suddenly as possible. The outer receiver, which, after the rarefaction, adhered strongly to the plate, is now loose, and the cupping-glass will be found sticking fast to it. While the rarefaction was going on, the air in the small receiver also expanded, escaped from it, and was abstracted by the pump. When the external air was suddenly admitted, it pressed on the small receiver, and forced it down to the plate, and thus shut up all entry. The small receiver must now adhere; and there can be no suction, for the pipe of the pump was on the outside of the cupping-glass.

This experiment sometimes does not succeed, because the air occasionally finds a passage under the brim of the cupping-glass. But if the cupping-glass be pressed down by the hand on the greasy leather or plate, everything will be made smooth, and the glass will be so little raised by the expansion of its air during the pumping, that it will instantly clap close when the air is re-admitted.

In like manner, if a thin square phial be furnished with a valve, opening from within, but shutting when pressed from without, and if this phial be put under a receiver, and the air be abstracted from the receiver, the air in the phial will expand during the rarefaction, escape through the valve, and lie at last in a very rarefied state within the phial. If the air be now admitted into the receiver, it will press on the flat sides of the included phial and crush it to pieces.

(See fig. 48.)

If a piece of wet ox-bladder be laid over the top of a receiver whose orifice is about four inches wide, and the air be exhausted from within it, the incumbent atmosphere will press down the bladder into a hollow form, and then burst it inward with a prodigious noise. (See fig. 49.) Or if a piece of thin flat glass be laid over the receiver, with an oiled leather between them to make the juncture air-tight, the glass will be broken downwards. This must be done with caution, because the pieces of glass sometimes fly about with great force.

If there be formed two hemispherical cups of brass, with very flat thick brims, and one of them be fitted with a neck and stopcock, as represented by fig. 50, the air may be abstracted from them by screwing the neck into the hole in the pump-plate. To prevent the insinuation of air, a ring of oiled leather may be put between them.

Now unscrew the sphere from the pump, and fix hooks to each, and suspend them from a strong nail, and hang a scale to the lowest. It will require a considerable weight to separate them; namely, about 15 pounds for every square inch of the great circle of the sphere. If this be four inches diameter, it will require near 190 pounds. This pretty experiment was first made by Otto Guericke, and on a very great scale. His sphere was of a large size, and when exhausted, the hemispheres could not be drawn asunder by 20 horses. It was exhibited, along with many others equally curious and magnificent, to the emperor of

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1 Such experiments should never be performed with a good pump; for fragments of the glass will get into the pump and impair its working, in spite of the utmost skill of the operator. Germany and his court, at the breaking up of the diet of Ratisbon in 1654. If a loaded syringe be suspended by its piston from the hook in the top plate of the receiver, as in fig. 51, and the air be abstracted by the pump, the syringe will gradually descend (because the elasticity of the air, which formerly balanced the pressure of the atmosphere, is now diminished by its expansion, and is therefore no longer able to press the syringe to the piston), and it will at last drop off. If the air be admitted before this happens, the syringe will immediately rise again.

Screw a short brass pipe into the neck of a transporter, on which is set a tall receiver, and immerse it into a cistern of water. On opening the cock, the pressure of the air on the surface of the water in the cistern will force it up through the pipe, and cause it to spout into the receiver with a strong jet, because there is no air within to balance by its elasticity the pressure of the atmosphere. (See fig. 52.)

It is in the same way that the gage of the air-pump performs its office. The pressure of the atmosphere raises the mercury in the gage till the weight of the mercury, together with the remaining elasticity of the air in the receiver, are in equilibrium with the whole pressure of the atmosphere; therefore the height and weight of the mercury in the gage is the excess of the weight of the atmosphere above the elasticity of the included air; and the deficiency of this height from that of the mercury in the Torricellian tube is the measure of this remaining elasticity.

If a Torricellian tube be put under a tall receiver, as shown in fig. 53, and the air be exhausted, the mercury in the tube will descend, while that in the gage will rise; and the sum of their heights will always be the same, that is, equal to the height in an ordinary barometer. The height of the mercury in the receiver is the effect and measure of the remaining elasticity of the included air, and the height in the pump-gage is the unbalanced pressure of the atmosphere. This is a very instructive experiment, perfectly similar to Mr. Auzout's, and completely establishes and illustrates the whole doctrine of atmospheric pressure.

We get a similar illustration and confirmation (if such a thing be now needed) of the cause of the rise of water in pumps, by screwing a syringe into the top plate of a receiver, which syringe has a glass pipe plunging into a small cup of water. (See fig. 54.) When the piston-rod is drawn up, the water rises in the glass pipe, as in any other pump, of which this is a miniature representation. But if the air has been previously exhausted from the receiver, there is nothing to press on the water in the little jar; and it will not rise in the glass pipe though the piston of the syringe be drawn to the top.

Analogous to the rise of water in pumps is its rise and motion in syphons. Suppose a pipe ABCD, fig. 55, bent at right angles at B and C, and having its two ends immersed in the cisterns of water A and D. Let the leg CD be longer than the leg BA, and let the whole be full of water. The water is pressed upwards at A with a force equal to the weight of the column of air EA reaching to the top of the atmosphere; but it is pressed downwards by the weight of the column of water BA. The water at D is pressed downwards by the weight of the column CD, and upwards by the weight of the column of air FD reaching to the top of the atmosphere. The two columns of air differ very little in their weight, and may without any sensible error be considered as equal. Therefore there is a superiority of pressure downwards at D, and the water will flow out there. The pressure of the air will raise the water in the leg AB, and thus the stream will be kept up till the vessel A is emptied as low as the orifice of the leg BA, provided that the height of AB is not greater than what the pressure of the atmosphere can balance, that is, does not exceed 32 or 33 feet for water, 30 inches for mercury, &c.

A syphon then will always run from that vessel whose surface is highest; the form of the pipe is indifferent, because the hydrostatal pressures depend on the vertical height only. It must be filled with water by some other contrivance, such as a funnel, or a pump applied a-top; and the funnel must be stopped up, otherwise the air would get in, and the water would fall in both legs.

If the syphon have equal legs, and be turned up at the ends, it will remain full of water, and be ready for use. One end of it need only be dipped into any vessel of water, and the water will then flow out at the other end of the syphon. This is called the Wittemberg syphon, and is represented in fig. 56.

What is called the syphon fountain, constructed on this principle, is shown in fig. 57, where AB is a tall receiver, standing in a wide basin DE, which is supported on the pedestal H, by the hollow pillar FG. In the centre of the receiver is a jet pipe C, and in the top a ground stopper A. Near the base of the pillar is a cock N, and in the pedestal is another cock O.

Fill the basin DE with water within half an inch of the brim. Then pour in water at the top of the receiver (the cock N being shut) till it is about half full, and then put in the stopper. A little water will run out into the vessel DE. But before it runs over, open the cock N, and the water will run into the cistern H; and by the time that the pipe C appears above water, a jet will rise from it, and continue as long as water is supplied from the basin DE. The passage into the base cistern may be so tempered by the cock N that the water within the receiver shall keep at the same height; and what runs into the base may be received from the cock O into another vessel, and returned into DE, to keep up the stream.

This pretty philosophical toy may be constructed in the following manner. BB, (fig. 58,) is the ferril or cap into its con which the receiver is cemented. From its centre descends construction the jet pipe Ca, sloping outwards, to give room for the dis- and opera-charge pipe bd of larger diameter, the lower extremity of which d fits tightly into the top of the hollow pillar FG.

The operation of the toy is easily understood. Suppose the distance from C to H (fig. 57,) three feet, which is about \( \frac{1}{4} \) of the height at which the atmosphere would support a column of water. The water poured into AB would descend through FG (the hole A being shut) till the air has

Expanding, and then it would stop. If the pipe Ca be now opened, the pressure of the air on the surface of the water in the cistern DE will cause it to spout through C to the height of three feet nearly, and the water will continue to descend through the pipe FG. By tempering the cock N so as to allow the water to pass through it as fast as it is supplied by the jet, the amusement may be continued a long time. It will stop at last, however; because, as the jet is made into rarefied air, a little air will be extricated from the water, which will gradually accumulate in the receiver, and diminish its rarefaction, which is the moving cause of the jet. This indeed is an inconvenience felt in every employment of syphons, so much the more remarkably as their top is higher than the surface of the water in the cistern of supply.

Cases of this employment of a syphon are not unfrequent. When water collected at A (fig. 59.) is to be conducted in a pipe to C, situated in a lower part of the country, it sometimes happens that the intervening ground is higher than the fountain-head as at B. A forcing pump is erected at A, and the water forced along the pipe. Once it runs out at C, the pump may be removed, and the water will continue to run on the syphon principle, provided BD do not exceed 33 feet. But the water in that part of the conduit which is above the horizontal plane AD, is in the same state as in a receiver of rarefied air, and gives out some of the air which is united with it. This gradually accumulates in the elevated part of the conduit, and at last chokes it entirely.

This combination of air with water is very distinctly seen by means of the air-pump. If a small glass containing cold water, fresh drawn from the spring, be exposed, as in fig. 60, under the receiver, and the air rarefied, small bubbles will be observed to form on the inner surface of the glass, or on the surface of any body immersed in it, which will increase in size, and then detach themselves from the glass and reach the top; as the rarefaction advances, the whole water begins to show very minute air-bubbles rising to the top; and this appearance will continue for a very long time, till it be completely disengaged. Warming the water will occasion a still farther separation of air, and a boiling heat will separate all that can be disengaged. The reason assigned for these air-bubbles first appearing on the surface of the glass, &c., is, that air is attracted by bodies, and adheres to their surface. This may be so. But it is more probably owing to the attraction of the water for the glass, which causes it to quit the air which it held in solution, in the same manner as we see it happen when it is mixed with spirits-of-wine, with vitriolic acid, &c., or when salts or sugar are dissolved in it. For if we pour out the water which has been parged of air by boiling in vacuo, and fill the glass with fresh water, we shall observe the same thing, although a film of the purified water was left adhering to the glass. In this case there can be no air adhering to the glass.

Water thus purged of air by boiling (or even without boiling) in vacuo, will again absorb air when exposed to the atmosphere. The best demonstration of this is to fill with this water a phial, leaving about the size of a pea not filled. Immerse this in a vessel of water, with the mouth undermost, by which means the air-bubble will mount up to the bottom of the phial. After some days standing in this condition, the air-bubble will be completely absorbed, and the vessel quite filled with water. A glass of beer placed under the receiver and treated in the same way will be almost wholly converted into froth by the escape of its fixed air, and will have lost entirely the prickling smartness which is so agreeable, and become quite vapid.

The air-pump gives us, in the next place, a great variety of experiments illustrative of the air's elasticity and expansibility. The very operation of exhaustion, as it is called, is an instance of its great expansibility. But this elasticity and expansibility is not palpably exhibited to view. The following experiments show it most distinctly. First, put a flaccid bladder, jut of the which the neck is firmly tied with a thread, under a air receiver, and work the pump. The bladder will gradually swell, and will even be fully distended. Upon readmitting the air into the receiver, the bladder gradually collapses again into its former dimensions; while the bladder is flaccid, the air within it is of the same density and elasticity with the surrounding air, and its elasticity balances the pressure of the atmosphere. When part of the air of the receiver is abstracted, the remainder expands so as still to fill the receiver; but by expanding, its elasticity is plainly diminished; for we see by the fact, that the elasticity of the air of the receiver no longer balances the elasticity of that in the bladder, as it no longer keeps it in its dimensions. The air in the bladder expands also; it expands till its diminished elasticity is again in equilibrium with the diminished elasticity of the air in the receiver; that is, till its density is the same. When all the wrinkles of the bladder have disappeared, its air can expand no more, although we continue to diminish the elasticity of the air of the receiver by further rarefaction. The bladder now tends to burst; and if it be pierced by a point or knife fastened to the slip-wire, the air will rush out, and the mercury descend rapidly in the gage.

If a phial or tube (fig. 61) be partly filled with water, and immersed in a vessel of water with the mouth downwards, the air will occupy the upper part of the phial. If this apparatus be put under a receiver, and the air be abstracted, the air in the phial will gradually expand, allowing the water to run out by its weight till the surface of the water be on a level within and without. When this is the case, we must grant that the density and elasticity of the air in the phial is the same with that in the receiver. When we work the pump again, we shall observe the air in the phial expand still more, and come out of the water in bubbles. Continuing the operation, we shall see the air continually escaping from the phial; when this is over, it shows that the pump can rarefy no more. If we now admit the air into the receiver, we shall see the water rise into the phial, and at last almost completely fill it, leaving only a very small bubble of air at the top. This bubble had expanded so as to fill the whole phial.

Every one must have observed a cavity at the big end of an egg between the shell and the white. The white and yolk are contained in a thin membrane or bladder which adheres loosely to the shell, but is detached from it at that part; and this cavity increases by keeping the egg in a dry place. One may form a judgment of its size, and therefore of the freshness of the egg, by touching it with the tongue; for the shell, where it is not in contact with the contents, will presently feel warm, being quickly heated by the tongue, whilst the rest of the egg will feel cold.

If a hole be made in the opposite end of the egg, and it be set on a little tripod, and put under a receiver, the expansion of the air in the cavity of the egg will force the contents through the hole till the egg be quite emptied; or, if nearly one-half of the egg be taken away at the other end, and the white and yolk taken out, and the shell be put under a receiver, and the air abstracted, the air in the cavity of the egg will expand, gradually detaching the membrane from the shell, till it causes it to swell out, and gives the whole the appearance of an entire egg. In like manner shrivelled apples and other fruits will swell in vacuo by the expansion of the air confined in their cavities.

If a piece of wood, a twig with green leaves, charcoal, plaster of Paris, &c., be kept under water in vacuo, a prodigious quantity of air will be extracted; and if we readmit the air into the receiver, it will force the water into the pores of the body. In this case the body will not swim in water as it did before, showing that the vegetable fibres are specifically heavier than water. It is found, however, that the air contained in the pith and bark, such as cork, is not all extricated in this way; and that much of it is contained in vesicles which have no outlet; being secreted into them in the process of vegetation, as it is secreted in the air-bladder of fishes, where it is generally found in a pretty compressed state, considerably denser than the surrounding air. The air-bladder of a fish is surrounded by circular and longitudinal muscles, by which the fish can compress the air still further; and, by ceasing to act with them, allow it to swell out again. It is in this manner that the fish can suit its specific gravity to its situation in the water, so as to have no tendency either to rise or sink; but if the fish be put into the receiver of an air-pump, the rarefaction of the air obliges the fish to act more strongly with these contracting muscles, in order to adjust its specific gravity; and if too much air has been abstracted from the receiver, the fish is no longer able to keep its air-bladder in the proper degree of compression. It becomes therefore too buoyant, and comes to the top of the water, and is obliged to struggle with its tail and fins in order to get down; frequently in vain. The air-bladder sometimes bursts, and the fish goes to the bottom, and can no longer keep above without the continual action of its tail and fins. When fishes die, they commonly float at top, their contractive action being now at an end. All this may in some degree be illustrated by a small half-blown bladder, to which is appended a bit of lead, just so heavy as to make it sink in water; when this is put under a receiver, and the air abstracted, the bubble will rise to the top; and, by nicely adjusting the rarefaction, it may be kept at any height.

The playthings called Cartesian devils are similar to this. They are hollow glass figures, having a small aperture in the lower part of the figures, as at the point of the foot; their weight is adjusted so that they swim upright in water. When put into a tall jar filled to the top, and having a piece of leather tied over it, they will sink in the water, by pressing on the leather with the ball of the hand. This, by compressing the water, forces some of it to enter into the figure, and makes it heavier than the water; for which reason it sinks, but rises again on removing the pressure of the hand. (See figs. 63 and 64.)

If a half-blown ox-bladder be put into a box, and great weights laid on it, and the whole be put under a receiver, and the air abstracted; the air will, by expanding, lift up the weights, though above an hundred pounds. (See fig. 65.)

By such experiments, the great expansibility of the air is abundantly illustrated, as its compressibility was formerly illustrated by means of the condensing syringe. We now see that the expansibility and compressibility of air are in two sets of experiments form an uninterrupted chain; and so sure is it that there is no particular state of the air's density where the air very compressible and expansible are remarkably dissimilar.

Air in its ordinary state expands; because its ordinary state is a state of compression by the weight of the atmosphere; and if there were a pit about thirty-three miles deep, the air at the bottom would probably be as dense as water; and if it were fifty miles deep, it would be as dense as gold, if it did not become a liquid before this depth; nay, if a bottle with its mouth undermost were immersed six miles under water, it would probably be as dense as water; we say probably, for this depends on the nature of its compressibility; that is, on the relation which subsists between the compression and the force which produces it.

This is the circumstance of its constitution, which we now proceed to examine; and it is evidently a very important between circumstance. We have long ago observed, that the great compressibility and permanent fluidity of air, observed in the vast variety of phenomena, is totally inexplicable, on the producing supposition that the particles of air are like so many balls of sponge or so many foot-balls. Give to those what compressibility you please, common air could no more be fluid than a mass of clay; it could no more be fluid than a mass of such balls pressed into a box. It may be demonstrated, that before a parcel of such balls, just touching each other, can be squeezed into half their present dimensions, their globular shape will be entirely gone, and each will have become a perfect cube, touching six other cubes with its whole surface; and these cubes will be strongly compressed together, so that motion could never be performed through among them by any solid body without a very great force. Whereas we know that in this state air is just as permeable to every body as the common air that we breathe. There is no way in which we can represent this fluidity to our imagination, but by conceiving air to consist of particles, not only discrete, but distant from each other, and actuated by repulsive forces, or something analogous to them. It is an idle subterfuge, to which some physicists have recourse, saying, that they are kept asunder by an intervening ether, or elastic fluid of any other name. This is only removing the difficulty a step farther off; for the elasticity of this fluid requires the same explanation; and therefore it is necessary, in obedience to the rules of just reasoning, to begin the inquiry here; that is, to determine from the phenomena what is the analogy between the distances of the particles and the repulsive forces exerted at these distances, proceeding in the same way as in the examination of planetary gravitation. We shall learn the analogy by attending to the analogy between the compressing force and the density.

For the density depends on the distance between the particles; the nearer they are to each other, the denser is the air. Suppose a square pipe one inch wide and eight inches long, shut at one end, and filled with common air; then suppose a plug so nicely fitted to this pipe that no air can pass by its sides; suppose this piston thrust down to within an inch of the bottom: it is evident that the air which formerly filled the whole pipe now occupies the space of one cubic inch, which contains the same number of particles as were formerly diffused over eight cubic inches.

The condensation would have been the same if the air which fills a cube whose side is two inches had been squeezed into a cube of one inch, for the cube of two inches also contains eight inches. Now, in this case it is evident that the distance between the particles would be reduced to its half in every direction. In like manner, if a cube whose side is three inches, and which therefore contains 27 inches, be squeezed into one inch, the distance of the particles will be one-third of what it was: in general the distance of the particles will be as the cube root of the space into which they are compressed. If the space be $\frac{1}{8}$, $\frac{1}{27}$, $\frac{1}{64}$, &c., of its former dimensions, the distance of the particles will be $\frac{1}{2}$, $\frac{1}{3}$, $\frac{1}{4}$, &c. Now the term density, in its strict sense, expresses the vicinity of the particles; thus, densi arbores are trees growing near each other. The measure of this vicinity therefore is the true measure of the density; and when 27 inches of air are compressed into one, we should say that it is three times as dense; but we say, that it is 27 times denser.

Density is therefore used in a sense different from its strictest acceptation; it expresses the comparative number of equidistant particles contained in the same bulk. This is also abundantly precise, when we compare bodies of the same kind, differing in density only; but we also say, that gold is 19 times denser than water, because the same bulk of it is 19 times heavier. This assertion proceeds on the assumption, or the fact, that every ultimate atom of terrestrial matter is equally heavy. A particle of gold may contain more or fewer atoms of matter than a particle of water. In such a case, therefore, the term density has little or no reference to the vicinity of the particles; and is only a term of comparison of other qualities or accidents. But when we speak of the respective densities of the same substance in its different states of compression, the word density is strictly connected with vicinity of particles, and we may safely take either of the measures. We shall abide by the common acceptation, and call that air eight times as dense which has eight times as many particles in the same bulk, although the particles are only twice as near to each other.

Thus then we see, that by observing the analogy between the compressing force and the density, we shall discover the analogy between the compressing force and the distance of the particles. Now the force which is necessary for compressing two particles of air to a certain vicinity is a proper measure of the elasticity of the particles corresponding to that vicinity or distance; for it balances it, and forces which balance must be esteemed equal. Elasticity is a distinctive name for that corpuscular force which keeps the particles at that distance; therefore observations made on the analogy between the compressing force and the density of air will give us the law of its corpuscular force, in the same way that observations on the simultaneous deflections of the planets towards the sun gives us the law of celestial gravitation.

But the sensible compressing forces which we are able to apply is at once exerted on unknown thousands of particles, whilst it is the law of action of a single particle that we want to discover. We must therefore know the proportion of the numbers of particles on which the compressing force is exerted. It is easy to see, that since the distance of the particles is as the cube root of the density inversely, the number of particles in physical contact with the compressing surface must be as the square of this root. Thus, when a cube of eight inches is compressed into one inch, and the particles are twice as near each other as they were before, there must be four times the number of particles in contact with each of the sides of this cubical inch; or, when we have pushed down the square piston of the pipe spoken of above to within an inch of the bottom, there will be four times the number of particles immediately contiguous to the piston, and resisting the compression; and in order to obtain the force really exerted on one particle, and the elasticity of that particle, we must divide the whole compressing force by 4. In like manner, if we have compressed air into $\frac{1}{3}$th of its former bulk, and brought the particles into $\frac{1}{3}$d of their former distance, we must divide the compressing force by 9.

In general, if $d$ express the density, $\frac{1}{\sqrt[3]{d}}$ will express the distance $x$ of the particles; $\frac{1}{\sqrt[3]{d^2}}$, or $d^{2/3}$ will express the vicinity or real density; and $d^{2/3}$ will express the number of particles acting on the compressing surface; and if $f$ express the accumulated external compressing force, $\frac{f}{d^{2/3}}$ will express the force acting on one particle; and therefore the elasticity of that particle corresponding to the distance $x$.

We now proceed to consider the experiments by which Compressibility of air is to be established. In order to examine the compressibility of air that is not rarer than the atmosphere at the surface of the Fig.66. earth, we employ a bent tube or syphon ABCD (fig. 66), hermetically sealed at A, and open at D. The short leg AB must be very accurately divided in the proportion of its solid contents, and fitted with a scale whose units denote equal increments, not of length, but of capacity. There are various ways of doing this; but it requires the most scrupulous attention, and without this the experiments are of no value. In particular, the arched form at A must be noticed. A small quantity of mercury must then be poured into the tube, and passed backwards and forwards till it stands (the tube being held in a vertical position) on a level at B and C. Then we are certain that the included air is of the same density with that of the contiguous atmosphere. Mercury is now poured into the leg DC, which will fill it,

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1 The first experiments to this purpose were those made by Mr. Boyle, published in his De Natura Doctrina de Aere contra Linum, and exhibited before the Royal Society the year before. Mariotte made experiments of the same kind, which were published in 1676 in his Essai sur la Nature de l'Air, and Traité des Mouvements des Eaux. The most copious experiments are those by Sulzer (Mem. Berlins. ix.) those by Fontana (Opuscula Physico-Mathematica), and those by Sir George Shuckburgh and General Roy in the Philosophical Transactions.

suppose to G, and will compress the air into a smaller space AE. Draw the horizontal line EF; the new bulk of the compressed air is evidently AE, measured by the adjacent scale, and the addition made to the compressing force of the atmosphere is the weight of the column GF. Produce GF downwards to H, till FH is equal to the height shown by a Toricellian tube filled with the same mercury; then the whole compressing force is HG. This is evidently the measure of the elasticity of the compressed air in AE, for it balances it. Now, pour in more mercury, and let it rise to g, compressing the air into A e. Draw the horizontal line ef, and make fh equal to FH; then Ae will be the new bulk of the compressed air, \( \frac{AB}{Ae} \) will be its new density, and \( \frac{hg}{Ae} \) will be the measure of the new elasticity. This operation may be extended as far as we please, by lengthening the tube CD, and taking care that it be strong enough to resist the great pressure. Great care must be taken to keep the whole in a constant temperature, because the elasticity of air is greatly affected by heat, and the change by any increase of temperature is different according to its density or compression.

The experiments of Boyle, Mariotte, Amontons, and others, were not extended to very great compressions, the density of the air not having been quadrupled in any of them; nor do they seem to have been made with very great nicety. It may be collected from them in general, that the elasticity of the air is very nearly proportioned to its density; and accordingly this law was almost immediately acquiesced in, and was called the Boylean law; it is accordingly assumed by almost all writers on the subject as exact. Of late years, however, there occurred questions in which it was of importance that this point should be more scrupulously settled, and the former experiments were repeated and extended. The result has been, that the compression of atmospheric air and most other gases increases rather faster than is strictly proportional to the pressure.

Considerable varieties and irregularities are to be observed in these experiments. It is extremely difficult to preserve the temperature of the apparatus, particularly of the leg AB, which is most handled. A great quantity of mercury must be employed; and it does not appear that philosophers have been careful to have it precisely similar to that in the barometer, which gives us the unit of compressing force and of elasticity. The mercury in the siphon as well as in the barometer should be pure and boiled. If the mercury in the siphon is adulterated with bismuth and tin, which it commonly is to a considerable degree, the compressing force, and consequently the elasticity, will appear greater than the truth. If the barometer has not been nicely filled, it will be lower than it should be, and the compressing force will appear too great, because the unit is too small; and this error will be most remarkable in the smaller compressions.

The greatest source of error and irregularity in the experiments is the very heterogeneous nature of the air itself. Air is a solvent of all fluids, all vapours, and perhaps of many solid bodies. It is highly improbable that the different compounds shall have the same elasticity, or even the same law of elasticity; and it is well known, that air loaded with water or other volatile bodies, is much more expansible by heat than pure air; nay, it would appear from many experiments, that certain determinate changes both of density and of temperature, cause air to let go the vapours which it holds in solution. Cold causes it to precipitate water, as appears in dew; so does rarefaction, as is seen in the receiver of an air-pump.

In general, it appears that the elasticity of air does not increase quite so fast as its density. This will be best seen by the following tables, calculated from the experiments of Mr. Sulzer. The column E in each set of experiments expresses the length of the column GH, the unit being FH, whilst the column D expresses \( \frac{AB}{AE} \).

| First set | Second set | Third set | |-----------|------------|-----------| | D | E | D | E | D | E | | 1-000 | 1-000 | 1-000 | 1-000 | 1-000 | 1-000 | | 1-001 | 1-002 | 1-003 | 1-004 | 1-005 | 1-006 | | 1-002 | 1-003 | 1-004 | 1-005 | 1-006 | 1-007 | | 1-003 | 1-004 | 1-005 | 1-006 | 1-007 | 1-008 | | 1-004 | 1-005 | 1-006 | 1-007 | 1-008 | 1-009 | | 1-005 | 1-006 | 1-007 | 1-008 | 1-009 | 1-010 |

There appears in these experiments to be 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 precautions, 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 siphon, which was 34 inches long, he boiled mercury in it, and filled it with mercury boiling hot. He took a tinslate 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 siphon into this vessel, keeping the open end far within it. By this means the short leg of the siphon was filled with very dry air. The other part was now joined, and boiled mercury put into the bend of the siphon; 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:

| First set | Second set | Third set | |-----------|------------|-----------| | D | E | D | E | D | E | | 1-000 | 1-000 | 1-000 | 1-000 | 1-000 | 1-000 | | 1-001 | 1-002 | 1-003 | 1-004 | 1-005 | 1-006 | | 1-002 | 1-003 | 1-004 | 1-005 | 1-006 | 1-007 | | 1-003 | 1-004 | 1-005 | 1-006 | 1-007 | 1-008 | | 1-004 | 1-005 | 1-006 | 1-007 | 1-008 | 1-009 |

Here it appears again in the clearest manner that the elasticities do not increase as fast as the densities, and the differences are even greater than in Mr. Sulzer's experiments. The second set contains the results of experiments which were made on very damp air in a warm summer's morning. In these it appears that the elasticities are almost precisely proportional to the densities + a small constant quantity, nearly 0·11, deviating from this rule chiefly between the densities 1 and 1·5, within which limits we have very nearly \( D = E^{0·09} \). 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 set shows the compression and elasticity 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 immersing 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 rarer than what we breathe; we must take a very different method for examining the elasticity of rarefied air.

Let \( gh \) (fig. 67) be a long tube, formed a-top into a cup, and of sufficient diameter to receive another smaller tube \( af \), open at first at both ends. Let the outer tube and cup be filled with mercury, which will rise in the inner tube to the same level. Let \( af \) now be stopped at \( a \). It contains air of the same density and elasticity with the adjoining atmosphere. Note exactly the space \( ab \) which it occupies. Draw it up into the position of fig. 68, and let the mercury stand in it at the height \( de \), whilst \( ce \) is the height of the mercury in the barometer. It is evident that the column \( de \) is in equilibrium between the pressure of the atmosphere and the elasticity of the air included in the space \( ad \). And since the weight of \( ce \) would be in equilibrium with the whole pressure of the atmosphere, the weight of \( cd \) is equivalent to the elasticity of the included air. Whilst therefore \( ce \) is the measure of the elasticity of the surrounding atmosphere, \( cd \) will be the measure of the elasticity of the included air; and since the air originally occupied the space \( ab \), and has now expanded into \( ad \),

we have \( \frac{ab}{cd} \) for the measure of its density. N.B.

\( ce \) and \( cd \) are measured by the perpendicular heights of the columns, but \( ab \) and \( ad \) must be measured by their solid capacities.

By raising the inner tube still higher, the mercury will also rise higher, and the included air will expand still farther, and we obtain another \( cd \), and another \( \frac{ab}{ad} \); and in this manner the relation between the density and elasticity of rarefied air may be discovered.

This examination may be managed more easily by means of the air-pump. Suppose a tube \( ae \) (fig. 69) containing a small quantity of air \( ab \), set up in a cistern of mercury, which is supported in the tube at the height \( eb \), and let \( ee \) be the height of the mercury in the barometer. Let this apparatus be set under a tubulated receiver on the pump-plate, and let \( gn \) be the pump-gage, and \( mn \) be made equal to \( ee \).

Then, as has been already shown, \( eb \) is the measure of the elasticity of the air in \( ab \), 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 \( ra \) 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. Another method.

Let an apparatus \( abcedef \) (fig. 70,) be made, consisting of a horizontal tube \( ae \) of even bore, a ball \( dg \) of a large diameter, and a swan-neck tube \( hf \). Let the ball and part of the tube \( ge \) 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 \( f \) with an air-pump. When the air is abstracted from the surface \( de \), the air in \( ab \) will expand into a larger bulk \( ac \), 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 receiver of an air-pump a glass vessel, having a very narrow mouth, over a cistern of mercury, and then abstract the air till the gage rises to some determined 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 further 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 \( v \) of the mercury, which would completely fill the whole vessel; then the natural bulk of the air will be \( v-w \), whilst 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 \( \frac{v-w}{w} \). And thus may the relation between density and elasticity in all cases be obtained.

A great variety of experiments to this purpose have been made, with different degrees of attention, according to the interest which the philosophers had in the result. Those made by M. de Luc, General Roy, Mr. Trembley, and Sir George Shuckburgh, are by far the most accurate; but they are all confined to very moderate rarefactions. The gene-

ral result has been, that the elasticity of rarefied air is very nearly proportional to its density. We cannot say with confidence that any regular deviation from this law has been observed, there being 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.

Let us, upon the whole, assume the Boylean law, viz. that the elasticity of the air is proportional to its density. The law deviates not in any sensible degree from the 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.

Let us now see what information this gives us with respect to the action of the particles on each other. The investigation is extremely easy. We have seen that a force eight times greater than the pressure of the atmosphere will compress common air into the 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 $\frac{1}{9}$ of its former bulk, the particles are at $\frac{1}{3}$ 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 $\frac{1}{x}$ be the distance of the particles, the number of them in any given vessel, and therefore the density will be as $x^3$, and the number pressing by their elasticity on its whole internal surface will be as $x^2$. Experiment shews, that the compressing force is as $x^3$, which being distributed over the number as $x^2$, will give the force on each as $x$. 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 corporeal repulsions exerted by the adjoining particles are inversely as their distances from each other, or that the adjoining particles tend to recede from each other with forces inversely proportional to their distances.

Sir Isaac Newton was the first who reasoned in this manner from the phenomena. Indeed he was the first who had the patience to reflect on the phenomena with any precision. His discoveries in gravitation naturally 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 second book of his Principles) several beautiful propositions, determining the mechanical constitution of the atmosphere.

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.

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 rarify 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 $\frac{24}{100}$ 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 further off. The question comes now to be, Whether, in the state of common air, they really do act five times further than the distance of the adjoining particles? Whilst the particle $a$ acts on the particle $b$ with the force $s$, does it also act on the particle $c$ with the force $2s$, 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 $1$, on the particle $g$ with the force $0-833$, &c.

Sir Isaac Newton shows in the plainest manner, that this is by no means the case; for if this were the case, he makes it appear that the sensible phenomena of condensation would be totally different from that we observe. The force necessary for a quadruple condensation would be eight times greater, and for a multiple 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 corporeal force is unlike everything we observe in nature, and to the last degree improbable.

We must therefore continue the limitation of this mutual 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 distances; 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.

And, in the first place, this view of the compressibility of the air must give us a very different notion of the height of the air of the atmosphere from what we deduced on a former occasion from our experiments. It is found, that when the air is of the temperature 32° of Fahrenheit's thermometer, and the mercury in the barometer 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 $30 \times 10 \times 87$ feet, or 5 miles and 100 yards. But the loose reasoning adduced on that occasion was enough to Height of the atmosphere.

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.

Let \( b \) (fig. 71) be the last particle of illuminated air which can be seen in the horizon by a spectator at \( A \). This must be illuminated by a ray \( SDb \), 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 \( E b S \) or \( ACD \) is 18 degrees; therefore \( bC \) is the secant of 9 degrees (it is less, viz. about 8½ degrees, on account of refraction). We know the earth's radius to be about 3970 miles; hence we conclude \( bB \) 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 the air is sufficiently dense for reflecting a sensible light at the height of nearly 200 miles.

We have now seen that air is prodigiously expansible. None of our experiments have distinctly shown us any limit to the air's expansibility. But it does not follow that it is expansible without end; nor is this at all likely. It is much more 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 we know precisely the law of this mutual repulsion, we cannot say what is the height of the atmosphere.

But if the air be an elastic fluid whose density is always proportional to the compressing force, we can tell what is its density at any height above the surface of the earth; and we can compare the density so calculated with the density discovered by observation: for this last is measured by the height at which it supports mercury in the barometer. This is the direct measure of the pressure of the external air; and as we know the law of gravitation, we can tell what would be the pressure of air having the calculated density in all its parts.

Let us therefore suppose a prismatic or cylindric column of air reaching to the top of the atmosphere. Let this be divided into an indefinite number of strata of very small and equal depths or thickness; and let us, for greater simplicity, suppose at first that a particle of air is of the same weight at all distances from the centre of the earth.

The absolute weight of any one of these strata will on these conditions be proportional to the number of particles or the gravity of air contained in it; and since the depth of each stratum is the same, this quantity of air will evidently be as the density of the stratum. But the density of any stratum is as the compressing force; that is, as the pressure of the strata above it; that is, as their weight; that is, as their quantity of matter: therefore the quantity of air in each stratum is proportional to the quantity of air above it. The quantity in each stratum, however, is the difference between the column incumbent on its bottom and on its top; therefore these differences are proportional to the quantities of which they are the differences. But when there is a series of quantities which are proportional to their own differences, both the quantities and the differences are in continual or geometrical progression: for let \( a, b, c \) be three such quantities that \( b = a - b = b - c \); then by alternation and composition \( a : b = b : c \); therefore the densities of these strata decrease in a geometrical progression; that is, when the elevations above the centre or surface of the earth increase, or their depths under the top of the atmosphere decrease, in an arithmetical progression, the densities decrease in a geometrical progression.

Let \( ARQ \) (fig. 72), represent the section of the earth by a plane through its centre \( O \), and let \( mOAM \) be a vertical line, and \( AE \) perpendicular to \( OA \) will be a horizontal line through \( A \), a point on the earth's surface. Let \( AE \) be taken to represent the density of the air at \( A \); and let \( DH \), parallel to \( AE \), be taken to \( AE \) as the density at \( D \) is to the density at \( A \): it is evident, that if a logistic or logarithmic curve \( EHIN \) be drawn, having \( AN \) for its axis, and passing through the points \( E \) and \( H \), the density of the air at any other point \( C \), in this vertical line, will be represented by \( CG \), the ordinate to the curve in that point: for it is the property of this curve, that if portions \( AB, AC, AD \), of its axis to be taken in arithmetical progression, the ordinates \( AE, BF, CG, DH \), will be in the geometrical progression.

It is another fundamental property of this curve, that if \( EK \) or \( HS \) touch the curve in \( E \) or \( H \), the subtangent \( AK \) or \( DS \) is a constant quantity.

And a third fundamental property is, that the infinitely extended area \( MAEN \) is equal to the rectangle \( KAEI \) of the ordinate and subtangent; and, in like manner, the area \( MDHN \) is equal to \( SD \times DH \), or to \( KA \times DH \); consequently the area lying beyond any ordinate is proportional to that ordinate.

These geometrical properties of this curve are all analogous to the chief circumstances in the constitution of the atmosphere, on the supposition of equal gravity. The area \( MCGN \) represents the whole quantity of aerial matter which is above \( C \). For \( CG \) is the density at \( C \), and \( CD \) is the thickness of the stratum between \( C \) and \( D \); and therefore \( CGHD \) will be as the quantity of matter or air in it; and in like manner of all the others, and of their sums, or the whole area \( MCGN \); and as each ordinate is proportional to the area above it, so each density, and the quantity of air in each stratum, is proportional to the quantity of air above it; and as the whole area \( MAEN \) is equal to the rectangle \( KAEI \), so the whole air of variable density above \( A \) might be contained in a column \( KA \), if, instead of being compressed by its own weight, it were without weight, and compressed by an external force equal to the pressure of the air at the surface of the earth. In this case, it would be of the uniform density \( AE \), which it has at the surface of the earth, making what we have repeatedly called the homogeneous atmosphere.

Hence we derive this important circumstance, that the height of the homogeneous atmosphere is the subtangent of that curve, the ordinates of which are as the densities of the air at different heights, on the supposition of equal gravity. This curve may with propriety be called the atmospherical

It may be done by comparing the densities of mercury and air. For a column of air of uniform density, reaching to the top of the homogeneous atmosphere, is in equilibrium with the mercury in the barometer. Now, it is found, by the best experiments, that when mercury and air are of the temperature of 32° of Fahrenheit's thermometer, and the barometer stands at 30 inches, the mercury is nearly 10440 times denser than air. Therefore the height of the homogeneous atmosphere is 10440 times 30 inches, or 25160 feet, or 8700 yards, or 4350 fathoms, or 5 miles wanting 100 yards.

Or it may be found by observations on the barometer. It is found, that when the mercury and air are of the above temperature, and the barometer on the sea-shore stands at 30 inches, if we carry it to a place 884 feet higher it will fall to 29 inches. Now, in all logarithmic curves having equal ordinates, the portions of the axes intercepted between the corresponding pairs of ordinates are proportional to the subtangents. And the subtangents of the curve belonging to our common tables is 0·0142943, and the difference of the logarithms of 30 and 29, (which is the portion of the axis intercepted between the ordinates 30 and 29), or 0·0147233, is to 0·0142945 as 883 is to 25068 feet, or 8686 yards, or 4343 fathoms, or 5 miles wanting 114 yards. This determination is 14 yards less than the other, and it is uncertain which is the more exact. It is extremely difficult to measure the respective densities of mercury and air; and in measuring the elevation which produces a fall of one inch in the barometer, an error of 1/20th of an inch would produce all the difference. We prefer the last, as depending on fewer circumstances.

But all this investigation proceeds on the supposition of equal gravity, whereas we know that the weight of a particle of air decreases as the square of its distance from the centre of the earth increases. In order, therefore, that a superior stratum may produce an equal pressure at the surface of the earth, it must be denser, because a particle of it gravitates less. The density, therefore, at equal elevations, must be greater than on the supposition of equal gravity, and the law of diminution of density must be different.

Make OD : OA = OA : Od; OC : OA = OA : Oc; OB : OA = OA : Ob; &c.; so that Od, Oc, Ob, OA, may be reciprocals to OD, OC, OB, OA; and through the points, A, b, c, d, draw the perpendiculars AE, bf, cg, dh, making them proportional to the densities in A, B, C, D; and let us suppose CD to be exceedingly small, so that the density may be supposed uniform through the whole stratum. Thus we have

\[ \frac{OD}{OC} = \frac{OA^2}{OC^2} \]

and \( \frac{OC}{Od} = \frac{OD}{OC} \);

or \( \frac{Oc}{Od} = \frac{OD}{OC} \);

and \( \frac{cd}{CD} = \frac{Od}{OD} \);

or, because OC and OD are ultimately in the ratio of equality, we have

\[ cd : CD = Oc : OC = OA^2 : OC^2, \]

and \( cd \times \frac{OA^2}{OC^2} = CD \times cg \times \frac{OA^2}{OC^2}; \) but

\[ CD \times cg \times \frac{OA^2}{OC^2} \] is as the pressure at C arising from the absolute weight of the stratum CD. For this weight is as the bulk, as the density, and as the gravitation of each particle jointly. Now CD expresses the bulk, cg the density, and \( \frac{OA^2}{OC^2} \) the gravitation of each particle. Therefore, \( cd \times cg \)

is as the pressure on C arising from the weight of the stratum DC; but \( cd \times cg \) is evidently the element of the curvilinear area AmeE, formed by the curve Efg h n and the ordinates AE, bf, cg, ah, &c. &c. Therefore the sum of all the elements, such as e d h g, that is, the area e m n g below eg, will be as the whole pressure on C, arising from the gravitation of all the air above it; but, by the nature of air, this whole pressure is as the density which it produces, that is, as cg. Therefore the curve Egn is of such a nature that the area lying below or beyond any ordinate cg is proportional to that ordinate. This is the property of the logarithmic curve, and E gn is a logarithmic curve.

But farther, this curve is the same with Egn. For let B continually approach to A, and ultimately coincide with it. It is evident that the ultimate ratio of BA to Ab, and of BP to bf, is that of equality; and if EFK, EJk, be drawn, they will contain equal angles with the ordinate AE, and will cut off equal subtangents AK, Ak. The curves Egn, Egn are therefore the same, but in opposite positions.

Lastly, if OA, Ob, Oc, Od, &c. be taken in arithmetical progression decreasing, their reciprocals OA, OB, OC, OD, &c. will be in harmonical progression increasing, as is well known; but, from the nature of the logarithmic curve, whose ordinates AE, bf, cg, dh, &c. are in geometrical progression. Therefore when OA, OB, OC, OD, &c. are in arithmetical progression, the densities of the air at A, B, C, D, &c. are in geometrical progression; and thus may the density of the air at all elevations be discovered. Thus, to find the density of the air at K the top of the homogeneous atmosphere, make OK : OA = OA : Od, and draw the ordinate dh, dh is the density at K.

The celebrated Dr. Halley was the first who observed the relation between the density of the air and the ordinates of the logarithmic curve, or common logarithms. This he did on the supposition of equal gravity; and his discovery is acknowledged by Sir Isaac Newton in his Principia, ii. prop. 22, schol. Halley's dissertation on the subject is in No. 185 of the Philosophical Transactions. Newton, with his usual sagacity, extended the same relation to the true state of the case, where gravity is as the square of the distance inversely; and showed that when the distances from the earth's centre are in harmonic progression, the densities are in geometric progression. He shows, indeed, in general, what progression of the distance, on any supposition of gravity, will produce a geometrical progression of the densities, so as to obtain a set of lines OA, Ob, Oc, Od, &c. which will be logarithms of the densities.

From these principles a corollary is deducible, viz., that the Probable air has a finite density at an infinite distance from the centre limit to application of the earth, which will be represented by the ordinate OP drawn through the centre. But from this corollary it would follow, that our moon must attract and acquire to itself a portion of this atmosphere, bearing an approximate relation to the gravity at its surface. Astronomy pronounces this highly improbable, and thus sets a practical limit to the law of compression equal to elasticity, on which our reasoning is founded.

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1. The subject was afterwards treated in a more familiar manner by Cotes in his Hydrostatic Lectures, and in his Harmonia Mensurarum; by Dr. Brook Taylor, in his Methodus Incrementi; by Wolf in his Aerometria; by Herman in his Phronemata; and by Horneby in the Philosophical Transactions, tom. Ixiv. We have thus given an elementary account of the distinguishing properties of air as a heavy and compressible fluid, and of the general phenomena which are immediate consequences of these properties. This we have done in a set of propositions analogous to those which form the doctrines of hydrostatics. It remains to consider it in another point of view, namely, as moveable and inert. The phenomena consequent on these properties are exhibited in the velocities which air acquires by pressure, in the resistance which bodies meet with to their motion through the air, and in the impression which air in motion gives to bodies exposed to its action.

We shall first consider the motions of which air is susceptible when the equilibrium of pressure, whether arising from its weight or its elasticity, is removed; and, in the next place, we shall consider its action on solid bodies exposed to its current, and the resistance which it makes to their motion through it. In this consideration we shall avoid the extreme of generality, which renders the discussion too abstract and difficult, and adapt our investigation to the circumstances in which compressible fluids, of which air is taken for the representative, are most commonly found. We shall consider air therefore as it is commonly found in accessible situations, as acted on by equal and parallel gravity; and we shall consider it in the same order in which water is treated in a system of hydraulics.

In that science the leading problem is to determine with what velocity the water will move through a given orifice when impelled by some known pressure; and it has been found, that the best form in which this most difficult and intricate proposition can be put, is to determine the velocity of water flowing through this orifice when impelled by its weight alone. Having determined this, we can reduce to this case every question which can be proposed, for in place of the pressure of any piston or other mover, we can always substitute a perpendicular column of water or air whose weight shall be equal to the given pressure.

The first problem, therefore, is to determine with what velocity air will rush into a void when impelled by its weight alone. This is evidently analogous to the hydraulic problem of water flowing out of a vessel. And here we must be contented with referring our readers to the solutions which have been given of that problem, and the demonstration that it flows with the velocity which a heavy body would acquire by falling from a height equal to the depth of the hole under the surface of the water in the vessel.

In whatever way we attempt to demonstrate that proposition, every step, nay, every word, of the demonstration applies equally to the air, or to any fluid whatever. Or, if our readers should wish to see the connexion or analogy of the cases, we only desire them to recollect an undoubted maxim in the science of motion, that "when the moving force and the matter to be moved vary in the same proportion, the velocity will be the same." If therefore there be similar vessels of air, water, oil, or any other fluid, all of the height of a homogeneous atmosphere, they will all run through equal and similar holes with the same velocity; for in whatever proportion the quantity of matter moving through the hole be varied by a variation of density, the pressure which forces it out, by acting in circumstances perfectly similar, varies in the same proportion by the same variation of density. We must therefore assume it as the leading proposition, that "air rushes from the atmosphere into a void with the velocity which a heavy body would acquire by falling from the top of a homogeneous atmosphere."

It is known that air is about 840 times lighter than water, and that the pressure of the atmosphere supports water at the height of 33 feet nearly. The height therefore of a homogeneous atmosphere is nearly $33 \times 840$, or 27,720 feet. Moreover, to know the velocity acquired by any fall, recollect that a heavy body by falling one foot acquires the velocity of 8 feet per second; and that the velocities acquired by falling through different heights are as the square roots of the heights. Therefore to find the velocity corresponding to any height, expressed in feet per second, multiply the square root of the height by 8. We have therefore in the present instance $V = 8\sqrt{27,720} = 8 \times 165.493 = 1332$ feet per second. This therefore is the velocity with which common air will rush into a void; and this may be taken as a standard number in pneumatics, as 16 and 32 are standard numbers in the general science of mechanics, expressing the action of gravity at the surface of the earth.

It is easy to see that greater precision is not necessary in this matter. The height of a homogeneous atmosphere is a variable thing, depending on the temperature of the air. If this reason seems any objection against the use of the number 1332, we may retain $8\sqrt{H}$ in place of it, where $H$ expresses the height of a homogeneous atmosphere of the given temperature. A variation of the barometer makes no change in the velocity, nor in the height of the homogeneous atmosphere, because it is accompanied by a proportional variation in the density of the air. When it is increased $\frac{1}{10}$, for instance, the density is also increased $\frac{1}{10}$; and thus the expelling force and the matter to be moved are changed in the same proportion, and the velocity remains the same. Observe, we do not here consider the velocity which the air acquires after its issuing into the void by its continual expansion. This may be ascertained by the 39th proposition of Newton's Principia, book first. Nay, which appears very paradoxical, if a cylinder of air, communicating in this manner with a void, be compressed by a piston loaded with a weight, which presses it down as the air flows out, and thus keeps it of the same density, the velocity of efflux will still be the same, however great the pressure may chance to be; for the first and immediate effect of the load on the piston is to reduce the air in the cylinder to such a density that its elasticity shall exactly balance the load; and because the elasticity of air is proportional to its density, the density of the air will be increased in the same proportion with the load, that is, with the expelling power, for we are neglecting at present the weight of the included air as too inconsiderable to have any sensible effect. Therefore, since the matter to be moved is increased in the same proportion with the pressure, the velocity will be the same as before.

It is equally easy to determine the velocity with which the air of the atmosphere will rush into a space containing city with rarer air. Whatever may be the density of this air, its which air elasticity, which follows the proportion of its density, will rush into a space containing and is the excess of this last only which is the rarer air, moving force. The matter to be moved is the same as before. Let $D$ be the natural density of the air, and $\delta$ the density of the air contained in the vessel into which it is supposed to run, and let $P$ be the pressure of the atmosphere, and therefore equal to the force which impels it into a void; and let $w$ be the force with which this rarer air would run into a void. We have $D : \delta = P : w$, and $w = \frac{PD}{\delta}$. Now the moving force in the present instance is $P - w$, or $P - \frac{PD}{\delta}$. Lastly, let $V$ be the velocity of air rushing into a void, and $v$ the velocity with which it will rush into this rarer air.

It is a theorem in the motion of fluids, that the pressures are as the squares of the velocities of efflux.

Therefore $P : P - \frac{PD}{\delta} = V^2 : v^2$. Hence we derive $v^2 = V^2$. The motion ceases when the air in the vessel has acquired the density of the external air; that is, when \( \delta = D \), or when \( t = \frac{C}{4\sqrt{HO}D} \times \sqrt{D} = \frac{C}{4\sqrt{HO}} \). Therefore the time of completely filling the vessel is \( \frac{C}{4\sqrt{HO}} \).

Let us illustrate this by an example in numbers.

Supposing then that air is 840 times lighter than water, and the height of the homogeneous atmosphere 27,720 feet, we have \( 4\sqrt{H} = 666 \). Let us further suppose the vessel to contain 8 cubic feet, which is nearly a wine hogshead, and that the hole by which the air of the ordinary density, which we shall make \( = 1 \), enters, is an inch square, or \( \frac{1}{4} \) of a square foot. Then the time in seconds of completely filling it will be \( \frac{8}{14400} \), or \( \frac{1152}{666} \), or 1.7297". If the hole is only \( \frac{1}{16} \) of a square inch, that is, if its side is \( \frac{1}{8} \) of an inch, the time of completely filling the hogshead will be 173" very nearly, or something less than three minutes.

If we make the experiment with a hole cut in a thin plate, we shall find the time greater nearly in the proportion of 63 to 100, for reasons obvious to all who have studied hydraulics. In like manner we can tell the time necessary for bringing the air in the vessel to \( \frac{1}{4} \)ths of its ordinary density. The only variable part of our fluent is the coefficient \( \sqrt{D-\delta} \), or \( \sqrt{1-\delta} \). Let \( \delta = \frac{3}{4} \), then \( \sqrt{1-\delta} = \sqrt{\frac{1}{4}} = \frac{1}{2} \); and the time is 86\( \frac{1}{2} \) very nearly when the hole is \( \frac{1}{16} \) of an inch wide.

Let us now suppose that the air in the vessel ABCD (fig. 73.) is compressed by a weight acting on the cover AD, which is moveable down the vessel, and is thus expelled into the external air.

The immediate effect of this external pressure is to compress the air and give it another density. The density \( D \) of the external air corresponds to its pressure \( P \). Let the additional pressure on the cover of the vessel be \( p \), and the density of the air in the vessel be \( d \). We shall have \( P : P + p = D : d \); and therefore \( p = P \times \frac{d-D}{D} \). Then, because the pressure which expels the air is the difference between the force which compresses the air in the vessel and the force which compresses the external air, the expelling force is \( p \). And because the quantities of motion are as the forces which similarly produce them, we shall have \( P : p = MV : mv \); where \( M \) and \( m \) express the quantities of matter expelled, \( V \) expresses the velocity with which air rushes into a void, and \( v \) expresses the velocity sought. But because the quantities of aerial matter which issue from the same orifice in a moment are as the densities and velocities jointly, we shall have \( MV : mv = DVV : dv^2 \); \( dv^2 \).

Therefore \( P : p = DV^2 : dv^2 \). Hence we deduce

\[ V = V \sqrt{\frac{d-D}{d}}. \]

We may have another expression of the velocity without considering the density. We had \( P : P + p = D : d \); therefore \( d = \frac{D \times P + p}{P} \), and \( d - D = \frac{D \times P + p}{P} - D, \)

Air in motion.

\[ \frac{D \times P + p - DP}{P} = \frac{d - D}{d} = \frac{D \times P + p - DP}{D \times P + p} = \frac{P + p - P}{P + p} \]

\[ = \frac{P}{P + p} \text{; therefore } e = V \times \sqrt{\frac{P}{P + p}} \]

which is a very simple and convenient expression.

Hitherto we have considered the motion of air as produced by its weight only. Let us now consider the effect of its elasticity.

Let ABCD (fig. 73) be a vessel containing air of any density \( D \). This air is in a state of compression; and if the compressing force be removed, it will expand, and its elasticity will diminish along with its density. Its elasticity in any state is measured by the force which keeps it in that state. The force which keeps common air in its ordinary density is the weight of the atmosphere, and is the same with the weight of a column of water 33 feet high. If therefore we suppose that this air, instead of being confined by the top of the vessel, is pressed down by a moveable piston carrying a column of water 33 feet high, its elasticity will balance this pressure as it balances the pressure of the atmosphere; and as it is a fluid, and propagates through every part the pressure exerted on any one part, it will press on any little portion of the vessel by its elasticity in the same manner as when loaded with this column.

The consequence of this reasoning is, that if the small portion of the vessel be removed, and thus a passage be made into a void, the air will begin to flow out with the same velocity with which it would flow when impelled by its weight alone, or with the velocity acquired by falling from the top of a homogeneous atmosphere, or 1332 feet in a second nearly.

But as soon as some air has come out, the density of the remaining air is diminished, and its elasticity is diminished; therefore, the expelling force is diminished. But the matter to be moved is diminished in the very same proportion, because the density and elasticity are found to vary according to the same law; therefore the velocity will continue the same from the beginning to the end of the efflux.

This may be seen in another way. Let \( P \) be the pressure of the atmosphere, which being the counter-balance and measure of the initial elasticity, is equal to the expelling force at the first instant. Let \( D \) be the initial density, and \( V \) the initial velocity. Let \( d \) be its density at the end of the time \( t \) of efflux, and \( v \) the contemporaneous velocity. It is plain that at the end of this time we shall have the expelling force \( = \frac{Pd}{D} \); for \( D : d = P : \pi \left( \frac{Pd}{D} \right) \).

These forces are proportional to the quantities of motion which they produce; and the quantities of motion are proportional to the quantities of matter \( M \) and \( m \) and the velocities \( V \) and \( v \) jointly; therefore we have \( P : \frac{Pd}{D} = MV : mv \).

But the quantities of matter which escape through a given orifice are as the densities and velocities jointly; that is, \( M : m = DV : de \); therefore \( P : \frac{Pd}{D} = DV^2 : de^2 \), and \( P \times de^2 = \frac{PdDV^2}{D} = PdV^2 \), and \( V^2 = v^2 \), and \( V = v \), and the velocity of efflux is constant. Hence follows, what appears very unlikely at first sight, that however much the air in the vessel is condensed, it will always issue into a void with the same velocity.

In order to find the quantity of aerial matter which will issue during any time \( t \), and consequently the density of the remaining air at the end of this time, we must get the rate of efflux. In the element of time \( t \) there issues (by what has been said above) the bulk \( 8\sqrt{HO}t \) (for the velocity \( V \) is constant); and therefore the quantity \( 8\sqrt{HO}dt \). On the other hand, the quantity of air at the beginning was \( CD \), \( C \) being the capacity of the vessel; and when the air has acquired the density \( d \), the quantity is \( Cd \); therefore the quantity which has run out in the time \( t \) must be the fluxion of \( CD - Cd \), or \( -Cd \). Therefore we have the equation

\[ 8\sqrt{HO}dt = -Cd \text{, and } t = \frac{-Cd}{8\sqrt{HO}} = \frac{C}{8\sqrt{HO}} \times \frac{-d}{d} \]

The fluent of this is \( t = \frac{C}{8\sqrt{HO}} \log_d \). This fluent must be so taken that \( t \) may be \( = 0 \) when \( d = D \). Therefore the correct fluent will be \( t = \frac{C}{8\sqrt{HO}} \log_d \frac{D}{d} \), for \( \log_d \frac{D}{d} = \log_1 \frac{D}{d} = 0 \).

We deduce from this, that it requires an infinite time for the whole air of a vessel to flow out of it into a void. N.B. By \( \log_d \), &c., is meant the hyperbolic logarithm of \( d \), &c.

Let us next suppose that the vessel, instead of letting out its air into a void, emits it into air of a less density, which remains constant during the efflux, as we may suppose to be the case when a vessel containing condensed air emits its air into the surrounding atmosphere. Let the initial density of the air in the vessel be \( \delta \), and that of the atmosphere \( D \).

Then it is plain that the expelling force is \( P : \frac{PD}{\delta} \), and that after the time \( t \) it is \( \frac{PD}{\delta} - \frac{PD}{\delta} \). We have therefore \( P \times \frac{PD}{\delta} : \frac{PD}{\delta} = MV : mv = V^2 : de^2 \). Whence we derive \( e = V \sqrt{\frac{d - D}{d - D}} \).

From this equation we learn that the motion will be at an end when \( d = D \); and if \( d = D \) there can be no efflux.

To find the relation between the time and the density let \( H \), as before, be the height producing the velocity \( V \) between the height producing the velocity of efflux \( v \) must be \( H \) the time and density \( \times \frac{d - D}{d - D} \), and the little parcel of air which will flow out in the time \( t \) will \( = 8\sqrt{HO}dt \times \frac{d - D}{d - D} \). On the other hand, it is \( = -Cd \).

Hence we deduce the fluxionary equation \( t = \frac{C}{8\sqrt{HO}} \times \frac{-d}{d - D} \). The fluent of this corrected so as to make \( t = 0 \) when \( d = \delta \), is \( t = \frac{C}{8\sqrt{HO}} \times \log \left( \frac{d - D}{d - D} \right) \).

And the time of completing the efflux, when \( d = D \), is \( t = \frac{C}{8\sqrt{HO}} \times \log \left( \frac{d - D}{d - D} \right) \).

Lastly, let ABCD, CFGH (fig. 74) be two vessels containing airs of different densities, and communicating by the orifice C; there will be a current from the vessel containing the denser air into that containing the rarer; suppose from ABCD into CFGH.

Let \( P \) be the elastic force of the air in \( \text{ABCD} \), \( Q \) its density, and \( V \) its velocity, and \( D \) the density of the air in \( \text{CFGH} \). And, after the time \( t \), let the density of the air in \( \text{ABCD} \) be \( q \), its velocity \( v \), and the density of the air in \( \text{CFGH} \) be \( \delta \). The ex- pelling force from \( \text{ABCD} \) will be \( P = \frac{PD}{Q} \) at the first in- stant, and at the end of the time \( t \) it will be \( \frac{Pq}{Q} - \frac{P\delta}{Q} \). Therefore we shall have \( P = \frac{PD}{Q} : \frac{Pq}{Q} - \frac{P\delta}{Q} = QV^2 : qv^2 \), which gives \( v = V \times \sqrt{\frac{(Q-q)}{q(Q-D)}} \), and the motion will cease when \( \delta = q \).

Let \( A \) be the capacity of the first vessel, and \( B \) that of the second. We have the second equation \( AQ + BD = \) \( Aq + B\delta \), and therefore \( \delta = \frac{A(Q-q) + BD}{qB(Q-D)} \). Substituting this value of \( \delta \) in the former value of \( v \), we have \( v = V \times \) \( \sqrt{\frac{Q(B(q-D) - A(q-q))}{qB(Q-D)}} \), which gives the relation be- tween the velocity \( v \) and the density \( q \).

In order to ascertain the time when the air in \( \text{ABCD} \) has acquired the density \( q \), it will be convenient to abridge the work by some substitutions. Therefore make \( Q(B+A) \) \( = M, BQD + BQ^2 = N, BQ - BD = R \) and \( \frac{N}{M} = m \). Then, proceeding as before, we obtain the fluxionary equation

\[ s\sqrt{HOq} \frac{\sqrt{Mq-N}}{\sqrt{R}} i = AQ - q = -AQ, \quad \text{whence } i = \] \[ \frac{AVR}{8\sqrt{HOVM}} \times \frac{q}{\sqrt{q^2-mq}} \]

of which the fluent, comple-

ed so that \( t = 0 \) when \( q = Q \), is \( t = \frac{AVR}{8\sqrt{HOVM}} \times \log \)

\[ \left( \frac{Q-\frac{1}{2}m+\sqrt{(Q^2-mq)}}{q-\frac{1}{2}m+\sqrt{(q^2-mq)}} \right) \]

Some of these questions are of difficult solution, and they are not of frequent use in the more important and usual ap- plications of the doctrines of pneumatics, at least in their present form. The cases of greatest use are when the air is expelled from a vessel by an external force, as when bel- lows are worked, whether of the ordinary form or consisting of a cylinder fitted with a movement piston. This last case merits a particular consideration; and, fortunately, the inves- tigation is extremely easy.

Let \( AD \) (fig. 73) be considered as a piston moving down- ward with the uniform velocity \( f \), and let the area of the piston be \( n \) times the area of the hole of efflux, then the ve- locity of efflux arising from the motion of the piston be \( nf \). Add this to the velocity \( V \) produced by the elasticity of the air in the first question, and the whole velocity will be \( V + nf \). It will be the same in the other. The problem is also freed from the consideration of the time of efflux. For this depends now on the velocity of the piston. It is still, however, a very intricate problem to ascertain the relation between the time and the density, even though the piston is moving uniformly: for at the beginning of the motion the air is of common density. As the piston descends, it both expels and compresses the air, and the density of the air in the vessel varies in a very intricate manner, as also its resistance or reaction on the piston. For this reason, a piston which moves uniformly by means of an external force, will never make an uniform blast by successive strokes; it will always be weaker at the be- ginning of the stroke. The best way for securing an uniform blast is to employ the external force only for lifting up the piston, and then to let the piston descend by its own weight.

In this way it will quickly sink down, compressing the air, till its density and corresponding elasticity exactly balance the weight of the piston. After this the piston will descend equally, and the blast will be uniform. These observations and theorems will serve to determine the initial velocity of the air in all important cases of its explosion. The philoso- pher will learn the rate of its efflux out of one vessel into another; the chemist will be able to calculate the quantities of the different gases which are employed in the curious ex- periments of the ingenious but unfortunate Lavoisier on combustion, and will find them extremely different from what he supposed; the engineer will learn how to propor- tion the motive force of his machine to the quantity of aerial matter which his bellows must supply. But it is not enough, for this purpose, that the air begin to issue in the proper quantity; we must see whether it be not affected by the cir- cumstances of its subsequent passage.

All the modifications of motion which are observed in Passage of water conduits take place also in the passage of air through pipes and holes of all kinds. There is the same diminution of quantity passing through a hole in a thin plate that is ob- served in water. We know that, abating the small effect of friction, water issues with the velocity acquired by falling from the surface; and yet if we calculate by this velocity and by the area of the orifice, we shall find the quantity of water deficient nearly in the proportion of 63 to 100. This is owing to the water pressing towards the orifice from all sides, which occasions a contraction of the jet. The same thing happens in the efflux of air. Also the motion of water is greatly impeded by all contractions of its passage. These obliges it to accelerate its velocity, and therefore require an increase of pressure to force it through them, and this in proportion to the squares of the velocities. Thus, if a ma- chine working a pump causes it to give a certain number of strokes in a minute, it will deliver a determined quantity of water in that time. Should it happen that the passage of the water is contracted to one half in any part of the ma- chine, a thing which frequently happens at the valves, the water must move through this contraction with twice the velocity that it has in the rest of the passage. This will re- quire four times the force to be exerted on the piston. Nay, if no part of the passage is narrower than the barrel of the pump, but on the contrary a part much wider, and if the con- duit be again contracted to the width of the barrel, an addi- tional force must be applied to the piston to drive the water through this passage, which would not have been necessary if the passage had not been widened in any part. It will require a force equal to the weight of a column of water of the height necessary for communicating a velocity, the square of which is equal to the difference of the squares of the velocities of the water in the wide and the narrow part of the conduit.

The same thing takes place in the motion of air, and there- fore all contractions and dilatations must be carefully avoid- ed, when we want to preserve the velocity unimpaired.

Air also suffers the same retardation in its motion along pipes. By not knowing, or not attending to that, engineers of the first reputation have been prodigiously disappointed in their expectations of the quantity of air which will be de- livered by long pipes. Its extreme mobility and lightness hindered them from suspecting that it would suffer any sen- sible retardation. Dr. Papin, a most ingenious man, pro- posed this as the most effectual method of transferring the action of a moving power to a great distance. Suppose, for instance, that it was required to raise water out of a mine by a water-machine, and that there was no fall of water nearer than a mile's distance. He employed this water to drive a piston, which should compress the air in a cylinder communicating, by a long pipe, with another cylinder at the mouth of the mine. This second cylinder had a piston in it, whose rod was to give motion to the pumps at the mine. He expected, that as soon as the piston at the water-machine had compressed the air sufficiently, it would cause the air in the cylinder at the mine to force up its piston, and thus work the pumps. Dr. Hooke made many objections to the method, when laid before the Royal Society, and it was much debated there. But dynamics was at this time an infant science, and very little understood. Newton had not then taken any part in the business of the society, otherwise the true objections would not have escaped his sagacious mind.

Notwithstanding Papin's great reputation as an engineer and mechanic, he could not bring his scheme into use in England; but afterwards, in France and in Germany, where he settled, he got some persons of great fortunes to employ him in this project; and he erected great machines in Auvergne and Westphalia for draining mines. But, so far from being effective machines, they would not even begin to move. He attributed the failure to the quantity of air in the pipe of communication, which must be condensed before it can condense the air in the remote cylinder. This indeed is true, and he should have thought of this earlier. He therefore diminished the size of this pipe, and made his water-machine exhaust instead of condensing, and had no doubt but that the immense velocity with which air rushes into a void would make a rapid and effectual communication of power. But he was equally disappointed here, and the machine at the mine stood still as before.

Nearly a century after this, a very intelligent engineer attempted a much more feasible thing of this kind at an iron-foundry in Wales. He erected a machine at a powerful fall of water, which worked a set of cylinder bellows, the blow-pipe of which was conducted to the distance of a mile and a half, where it was applied to a blast furnace. But notwithstanding every care to make the conducting pipe very air-tight, of great size, and as smooth as possible, it would hardly blow out a candle. The failure was ascribed to the impossibility of making the pipe air-tight. But, what was surprising, above ten minutes elapsed after the action of the pistons in the bellows before the least wind could be perceived at the end of the pipe; whereas the engineer expected an interval of six seconds only.

No very distinct theory can be delivered on this subject; but we may derive considerable assistance in understanding the causes of the obstruction to the motion of water in long pipes, by considering what happens to air. The elasticity of the air, and its great compressibility, have given us the distinctest notions of fluidity in general, shewing us, in a way that can hardly be controverted, that the particles of a fluid are kept at a distance from each other, and from other bodies, by the corpuscular forces.

The writers on hydrodynamics have always considered the obstruction to the motion of fluids along canals of any kind, as owing to something like the friction by which the motion of solid bodies on each other is obstructed; but we cannot form to ourselves any distinct notion of resemblance, or even analogy between them. The fact is, however, that a fluid running along a canal has its motion obstructed; and that this obstruction is greatest in the immediate vicinity of the solid canal, and gradually diminishes to the middle of the stream. It appears, therefore, that the parts of fluids can no more move among each other than among solid bodies, without suffering a diminution of their motion. The parts in physical contact with the sides and bottom are retarded by these immovable bodies. The particles of the next stratum of fluid cannot preserve their initial velocities without overpowering the particles of the first stratum; and it appears from the fact that they are by this means retarded. They retard in the same manner the particles of the third stratum, and so on to the middle stratum or thread of fluid. It appears from the fact, therefore, that this sort of friction is not a consequence of rigidity alone, but that it is equally competent to fluids. Nay, since it is a matter of fact in air, and is even more remarkable there than in any other fluid, as we shall see by the experiments which have been made on the subject; and as our experiments on the compression of air show us the particles of air ten times nearer to each other in some cases than in others (viz. when we see air a thousand times denser in these cases), and therefore force us to acknowledge that they are not in contact; it is plain that this obstruction has no analogy to friction, which supposes roughness or inequality of surface. No such inequality can be supposed in the surface of an aerial particle; nor would it be of any service in explaining the obstruction, since the particles do not rub on each other, but pass each other at some small and imperceptible distance. We must therefore have recourse to some other mode of explication. We shall apply this to air only in this place; and, since it is proved by the incontrovertible experiments of Canton, Zimmerman, and others, that water, mercury, oil, &c., are also compressible and perfectly elastic, the argument from this principle, which is conclusive in air, must equally explain the similar phenomenon in hydraulics.

The most highly polished body which we know must be particles conceived as having an uneven surface when we compare it of air resist with the small spaces in which the corpuscular forces are a charge exerted; and a quantity of air moving in a polished pipe may from a rec- compared to a quantity of small shot sliding down a chan- an undula- nel with undulated sides and bottom. The row of particles ting im- immediately contiguous to the sides will therefore have an tion. undulated motion; but this undulation of the contiguous particles of air will not be so great as that of the surface along which they glide; for not only every motion requires force to produce it, but also every change of motion. The particles of air resist this change from a rectilinial to an undulating motion; and, being elastic, that is, repelling each other and other bodies, they keep a little nearer to the sur- face as they are passing over an eminence, and their path is less incurvated than the surface. The difference between the motion of the particles of air and the particles of a fluid quite unelastic is, in this respect, somewhat like the differ- ence between the motion of a spring-carriage and that of a common carriage. When the common carriage passes along a road not perfectly smooth, the line described by the cen- tre of gravity of the carriage keeps perfectly parallel to that described by the axis of the wheels, rising and falling along with it. Now let a spring body be put on the same wheels and pass along the same road. When the axis rises over an eminence perhaps half an inch, sinks down again into the next hollow, and then rises a second time, and so on, the centre of gravity of the body describes a much straighter line; for upon the rising of the wheels, the body resists the motion, and compresses the springs, and thus remains lower than it would have been had the springs not been inter- posed. In like manner, it does not sink so low as the axle does when the wheels go into a hollow. And thus the mo- tion of spring-carriages becomes less violently undulated than the road along which they pass. This illustration will, we hope, enable the reader to conceive how the deviation of the particles next to the sides and bottom of the canal from a rectilinial motion is less than that of the canal itself.

It is evident that the same reasoning will prove that the undulation of the next row of particles will be less than that of the first, that the undulation of the third row will be less than that of the second, and so on, as is represented in fig. 75. And thus it appears, that whilst the mass of air has a progressive motion along the pipe or canal, each par- ticle is describing a waving line, of which a line parallel to the direction of the canal is the axis, cutting all these undulations. This axis of each undulated path will be straight or curved as the canal is, and the excursions of the path on each side of its axis will be less and less as the axis of the path is nearer to the axis of the canal. Let us now see what sensible effect this will have; for all the motion which we here speak of is imperceptible. It is demonstrated in mechanics, that if a body moving with any velocity be deflected from its rectilineal path by a curved and perfectly smooth channel, to which the rectilineal path is a tangent, it will proceed along this channel with undiminished velocity. Now the path, in the present case, may be considered as perfectly smooth, since the particles do not touch it. It is one of the undulations which we are considering, and we may at present conceive this as without any subordinate inequalities. There should not, therefore, be any diminution of the velocity. Let us grant this of the absolute velocity of the particle; but what we observe is the velocity of the mass, and we judge of it perhaps by the motion of a feather carried along by it. Let us suppose a single atom to be a sensible object, and let us attend to two such particles, one at the side, and the other in the middle; although we cannot perceive the undulations of these particles during their progressive motions, we see the progressive motions themselves. Let us suppose, then, that the middle particle has moved without any undulation whatever, and that it has advanced ten feet. The lateral particle will also have moved ten feet; but this has not been in a straight line. It will not be so far advanced, therefore, in the direction of the canal; it will be left behind, and will appear to us to have been retarded in its motion; and in like manner each thread of particles will apparently be more and more retarded, as it recedes farther from the axis of the canal, or what is usually called the thread of the stream.

And thus the observed fact is shown to be a necessary consequence of what we know to be the nature of a compressible or elastic fluid; and that without supposing any diminution in the real velocity of each particle, there will be a diminution of the velocity of the sensible threads of the general stream, and a diminution of the whole quantity of air which passes along it during a given time.

Let us now suppose a parcel of air impelled along a pipe, which is perfectly smooth, out of a larger vessel, and issuing from this pipe with a certain velocity. It requires a certain force to change its velocity in the vessel to the greater velocity which it has in the pipe. This is abundantly demonstrated. How long sooner we suppose this pipe, there will be no change in the velocity, or in the force to keep it up. But let us suppose that about the middle of this pipe there is a part of it which has suddenly got an undulated surface, however imperceptible. Let us further suppose that the final velocity of the middle thread is the same as before. In this case it is evident that the sum total of the motions of all the particles is greater than before, because the absolute motions of the lateral particles is greater than that of the central particle, which we suppose the same as before. This absolute increase of motion cannot be without an increase of propelling force; the force acting now, therefore, must be greater than the force acting formerly. Therefore, if only the former force had continued to act, the same motion of the central particle could not have been preserved, or the progressive motion of the whole stream must be diminished. And thus we see that this internal insensible undulatory motion becomes a real obstruction to the sensible motion which we observe, and occasions an expense of power.

Let us see what will be the consequence of extending this obstructing surface further along the canal. It must evidently be accompanied by an augmentation of the motion produced, if the central velocity be still kept up; for the particles which are now in contact with the sides do not continue to occupy that situation. The middle particles moving faster forward get over them, and in their turn come next the side; and as they are really moving equally fast, but not in the direction into which they are now to be forced, force is necessary for changing the direction also; and this is in addition to the force necessary for producing the undulations so minutely treated of. The consequence of this must be, that an additional force will be necessary for preserving a given progressive motion in a longer obstructing pipe, and that the motion produced in a pipe of greater length by a given force will be less than in a shorter one, and the efflux will be diminished.

There is another consideration which must have an influence here. Nothing is more irrefragably demonstrated than the necessity of an additional force for producing an efflux through any contraction, even though it should be succeeded by a dilatation of the passage. Now both the inequalities of the sides and the undulations of the motions of each particle are equivalent to a succession of contractions and dilatations; although each of these is next to infinitely small, their number is also next to infinitely great, and therefore the total effect may be sensible.

We have hitherto supposed that the absolute velocity of the particles was not diminished; this we did, having assumed that the interval of each undulation of the sides was without inequalities. But this was gratuitous; it was also gratuitous that the sides were only undulated. We have no reason for excluding angular asperities. These will produce, and most certainly often produce, real diminutions in the velocity of the contiguous particles; and this must extend to the very axis of the canal, and produce a diminution of the sum total of motion; and in order to preserve the same sensible progressive motion, a greater force must be employed. This is all that can be meant by saying that there is a resistance to the motion of air through long pipes.

There remains another cause of diminution, viz. the want of perfect fluidity, whether arising from the dissemination of solid particles in a real fluid, or from the viscosity of the fluid. We shall not insist on this at present, because it cannot be shown to obtain in air, at least in any case which deserves consideration. It seems of no importance to determine the motion of air hurrying along with its soot or dust. The effect of fogs on a particular modification of the motion of air will be considered under another head. What has been said on this subject is sufficient for our purpose, as explaining the prodigious and unexpected obstruction to the passage of air through long and narrow pipes. We are able to collect an important maxim from it, viz. that all pipes of communication should be made as wide as circumstances will permit; for it is plain that the obstruction depends on the internal surface, and the force to overcome it must be in proportion to the mass of matter which is in motion. The first increases as the diameter of the pipe, and the last as the square. The obstruction must therefore bear a greater proportion to the whole motion in a small pipe than in a large one.

It were very desirable to know the law by which the retardation extends from the axis to the sides of the canal, retardation and the proportion which subsists between the lengths of unknowns, the canal and the forces necessary for overcoming the obstructions when the velocity is given; as also whether the proportion of the obstruction to the whole motion varies with the velocity; but all this is unknown. It does not, however, seem a desperate case in air; we know pretty distinctly the law of action among its particles, viz. that their mutual repulsions are inversely as their distances. This promises to enable us to trace the progress of undulation from the sides of the canal to the axis.

We can see that the retardations will not increase so fast as the square of the velocity. Were the fluid incompressible, so that the undulatory path of a particle were invariable, the deflecting forces by which each individual particle the velocity is made to describe its undulating path would be precisely the same as arise from the path itself and the motion in it; for each particle would be in the situation of a body moving along a fixed path. But in a very compressible fluid, such as air, each particle may be considered as a solitary body, actuated by a projectile and a transverse force, arising from the action of the adjoining particles. Its motion must depend on the adjustment of these forces, in the same manner as the elliptical motion of a planet depends on the adjustment of the force of projection, with a gravitation inversely proportional to the square of the distance from the focus. The transverse force in the present case has its origin in the pressure on the air which is propelling it along the pipe; this, by squeezing the particles together, brings their mutual repulsion into action. Now it is the property of a perfect fluid, that a pressure exerted on any part of it is propagated equally through the whole fluid; therefore the transverse forces which are excited by this pressure are proportional to the pressure itself; and we know that the pressures exerted on the surface of a fluid, so as to expel it through any orifice, or along any canal, are proportional to the squares of the velocities which they produce. Therefore, in every point of the undulatory motion of any particle, the transverse force by which it is deflected into a curve is proportional to the square of its velocity. When this is the case, a body would continue to describe the same curve as before; but, by the very compression, the curvatures are increased, supposing them to remain similar. This would require an increase of the transverse forces; but this is not to be found; therefore the particle will not describe a similar curve, but one which is less incurvated in all its parts; consequently the progressive velocity of the whole, which is the only thing perceivable by us, will not be so much diminished; that is, the obstructions will not increase so fast as they would otherwise do, or as the squares of the velocities.

This reasoning is equally applicable to all fluids, and is abundantly confirmed by experiments in hydraulics, as we shall see when considering the motion of rivers. We have taken this opportunity of delivering our notions on this subject; because, as we have often said, it is in the avowed discrete constitution of air that we see most distinctly the operation of those natural powers which constitute fluidity in general.

We would beg leave to mention a form of experiment for discovering the law of retardation with considerable accuracy. Experiments have been made on pipes and canals. M. Bossut, in his Hydrodynamique, has given a very beautiful set made on pipes of an inch and two inches in diameter, and 200 feet in length; but although these experiments are very instructive, they do not give us any rule by which we can extend the result to pipes of greater length and different diameters.

Let a smooth cylinder be set upright in a very large vessel or pond, and be moveable round its axis; let it be turned round by means of a wheel and pulley with an uniform motion and determined velocity. It will exert the same force on the contiguous water which would be exerted on it by water turning round it with the same velocity; and as this water would have its motion gradually retarded by the fixed cylinder, so the moving cylinder will gradually communicate motion to the surrounding water. We should observe the water gradually dragged round by it; and the vortex would extend farther and farther from it as the motion is continued, and the velocities of the parts of the vortex will be less and less as we recede from the axis. Now, we apprehend, that when a point of the surface of the cylinder has moved 200 feet, the motion of the water at different distances from it will be similar and proportional to, if not precisely the same with, retardations of water flowing 200 feet at the same distance from the side of a canal; at any rate, the two are susceptible of an accurate comparison, and the law of retardation may be accurately deduced from observations made on the motions of this vortex.

Air in motion is a very familiar object of observation; and it is interesting. In all languages it has got a name; we call it wind; and it is only upon reflection that we consider air as wind in a quiescent state. Many persons hardly know what is meant when air is mentioned; but they cannot refuse that the blast from a bellows is the expulsion of what they contained; and thus they learn that wind is air in motion.

It is of consequence to know the velocity of wind; but the velocity good and unexceptionable method has been contrived for this purpose. The best seems to be by measuring the space passed over by the shadow of a cloud; but this is extremely fallacious. In the first place, it is certain, that although we suppose that the cloud has the velocity of the air in which it is carried along, this is not an exact measure of the current on the surface of the earth; we may be almost certain that it is greater; for air, like all other fluids, is retarded by the sides and bottom of the channel in which it moves. But, in the next place, it is very gratuitous to suppose, that the velocity of the cloud is the velocity of the stratum of air between the cloud and the earth; we are almost certain that it is not. It was clearly proved by Dr. Hutton of Edinburgh, that clouds are always formed when two parcels of air of different temperatures mix together, each containing a proper quantity of vapour in the state of chemical solution. We know that different strata of air will frequently flow in different directions for a long time. In 1781, whilst a great fleet rendezvoused in Leith Roads during the Dutch war, there was a brisk easterly wind for about five weeks; and, during the last fortnight of this period, there was a brisk westerly current at the height of about three-fourths of a mile. This was distinctly indicated by frequent fleecy clouds at a great distance above a lower stratum of these clouds, which were driving all this time from the eastward. A gentleman who was present at the siege of Quebec in 1759, stated that one day whilst there blew a gale from the west, so hard that the ships at anchor in the river were obliged to strike their topmasts, and it was with the utmost difficulty that some well-manned boats could row against it, carrying some artillery stores to a post above the town, several shells were thrown from the town to destroy the boats; one of the shells burst in the air near the top of its flight, which was about half a mile high. The smoke of this bomb remained in the same spot for above a quarter of an hour, like a great round ball, and gradually dissipated by diffusion, without removing many yards from its place. When, therefore, two strata of air come from different quarters, and one of them flows over the other, it will be only in the contiguous surfaces that a precipitation of vapour will be made. This will form a thin fleecy cloud; and it will have a velocity and direction which neither belongs to the upper nor to the lower stratum of air which produced it. Should one of these strata come from the east and the other from the west with equal velocities, the cloud formed between them will have no motion at all; should one come from the east, and the other from the north, the cloud will move from the north-east with a greater velocity than either of the strata. So uncertain then is the information given by the clouds either of the velocity or the direction of the wind. A thick smoke from a furnace will give us a much less equivocal measure; and this, combined with the effects of the wind in impelling bodies, or deflecting a loaded plane from the perpendicular, or other effects of this kind, may give us measures of the different currents of wind with a precision sufficient for all practical uses.

The celebrated engineer, Mr. John Smeaton, has given, The result in the 51st volume of the Philosophical Transactions, the of Sme- velocities of wind corresponding to the usual denominations ton's observations made by himself in the course of his practice in erecting wind-mills. They are contained in the following table:— One of the most ingenious and convenient methods for Dr. Lind's measuring the velocity of the wind is to employ its pressure in supporting a column of water, in the same way as Mr. Pitot measures the velocity of a current of water. We believe that it was first proposed by Dr. James Lind of Windsor, a gentleman eminent for his great knowledge in all the branches of natural science, and for his ingenuity in every matter of experiment or practical application.

His anemometer consists of a glass tube of the form ABCD (fig. 76), open at both ends, and having the branch AB at right angles to the branch CD. This tube contains a few inches of water or any fluid (the lighter the better); it is held with the part CD upright, and AB horizontal and in the direction of the wind; that is, with the mouth A facing the wind. The wind acts in the way of pressure on the air in AB, compresses it, and causes it to press on the surface of the liquor; forcing it down to F; whilst it rises to E in the other leg. The velocity of the wind is concluded from the difference EF between the heights of the liquor in the legs. As the wind does not generally blow with uniform velocity, the liquor is apt to dance in the tube, and render the observation difficult and uncertain; to remedy this, it is proper to contract very much the communication at C between the two legs. If the tube has half an inch of diameter, and it should not have less, a hole of 1-50th of an inch is large enough; indeed the hole can hardly be too small, nor the tubes too large.

This instrument is extremely ingenious, and will undoubtedly give the proportions of the velocities of different currents with the greatest precision; for in whatever way the pressure of wind is produced by its motion, we are certain that the different pressures are as the squares of the velocities; if, therefore, we can obtain one certain measure of the velocity of the wind, and observe the degree to which the pressure produced by it raises the liquor, we can at all other times observe the pressures and compute the velocities from them, making proper allowances for the temperature and the height of the mercury in the barometer; because the velocity will be in the subduplicate ratio of the density of the air inversely when the pressure is the same.

It is usually concluded, that the velocity of the wind is that which would be acquired by falling from a height which is to EF as the weight of water is to that of an equal bulk of air. Thus, supposing air to be 840 times lighter than water, and that EF is 9-10ths of an inch, the velocity will be about 63 feet per second, which is that of a very hard gale, approaching to a storm. Hence we see by the bye, that the scale of this instrument is extremely short, and that it would be a great improvement of it to make the leg CD not perpendicular, but very much sloping; or perhaps the following form of the instrument will give it all the perfection of which it is capable. Let the horizontal branch AB (fig. 77) be contracted at B, and continued horizontally for several inches BG of a much smaller bore, and then turned down for two or three inches GC, and then upwards with a wide bore. To use the instrument, hold it with the part DC perpendicular; and (having sheltered the mouth A from the wind) pour in water at D till it advances along GB to the point B, which is made the beginning of the scale; the water in the upright branch standing at F in the same horizontal line with BG. Now, turn the mouth A to the wind; the air in AB will be compressed and will force the water along BG to F, and cause it to rise from F to E; and the range FE will be to the range BF on the scale as the section of the tube BG to that of CD. Thus, if the width of DC be half an inch, and that of BG 1-10th, we shall have 25 inches in the scale for one inch of real pressure EF.

But it has not been demonstrated in a very satisfactory manner, that the velocity of the wind is that acquired by falling through the height of a column of air whose weight is equal to that of the column of water EF. Experiments made with Pitot's tube in currents of water show that several corrections are necessary for conducting the velocity of the current from the elevations in the tube; these corrections may however be made, and safely applied to the present case; and then the instrument will enable us to conclude the velocity of the wind immediately, without any fundamental comparison of the elevation, with a velocity actually determined upon other principles. The chief use which we have for this information is in our employment of wind as an impelling power, by which we can actuate machinery or navigate ships. These are very important applications of pneumatical doctrines, and merit a particular consideration; and this naturally brings us to the last part of our subject, viz. the consideration of the impulse of air on bodies exposed to its action, and the resistance which it opposes to the passage of bodies through it.

This is a subject of the greatest importance, being the foundation of that art which has done the greatest honour to the ingenuity of man, and the greatest service to human society, by connecting together the most distant inhabitants of this globe, and making a communication of benefits which would otherwise have been impossible; we mean the art of Navigation or Seamanship. Of all the machines which human art has constructed, a ship is not only the greatest and most magnificent, but also the most ingenious and intricate; and the clever seaman possesses a knowledge founded on the most difficult and abstruse doctrines of mechanics. The seaman probably cannot give any account of his own science; and he possesses it rather by a kind of intuition than by any process of reasoning; but the success and efficiency of all the mechanism of this complicated engine, and the propriety of all the manoeuvres which the seaman practises, depend on the invariable laws of mechanics; and a thorough knowledge of these would enable an intelligent person not only to understand the machine and the manner of working it, but to improve both.

Unfortunately this is a subject of very great difficulty; and although it has employed the genius of Newton, who has con-

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1 See, on the subject of Anemometry, article Meteorology, paragraphs 81 to 83. Velocity of sidere it with great care, and his followers have added more to his labours on this subject than on any other; it still remains in a very imperfect state. A minute discussion of this subject cannot therefore be expected in a work like this; we must content ourselves with such a general statement of the most approved doctrine on the subject as shall enable our readers to conceive it distinctly, and judge with intelligence and confidence of the practical deductions which may be made from it.

Suppose then a plane surface, of which AC (fig. 78) is the section, exposed to the action of a stream of wind blowing in the direction QC, perpendicular to AC. The motion of the wind will be obstructed, and the surface AC pressed forward. And as all impulse or pressure is exerted in a direction perpendicular to the surface, and is resisted in the opposite direction, the surface will be impelled in the direction CD, the continuation of QC. And as the mutual actions of bodies depend on their relative motions, the force acting on the surface AC will be the same, if we shall suppose the air at rest, and the surface moving equally swift in the opposite direction. The resistance of the air to the motion of the body will be equal to the impulse of the air in the former case. Thus resistance and impulse are equal and contrary.

If the air be moving twice as fast, its particles will give a double velocity; but in this case a double number of particles will exert their impulse in the same time. The impulse will therefore be fourfold, and in general it will be as the square of the velocity; or if the air and body be both in motion, the impulse and resistance will be proportional to the square of the relative velocity. This is the first proposition on the subject, and it appears very consistent to reason. There will therefore be some analogy between the force of the air's impulse or the resistance of a body, and the weight of a column of air incumbent on the surface; for it is a principle in the action of fluids, that the heights of the columns of fluid are as the squares of the velocities which their pressures produce. Accordingly, the second proposition is, that the absolute impulse of a stream of air, blowing perpendicularly on any surface, is equal to the weight of a column of air which has that surface for its base, and for its height the space through which a body must fall in order to acquire the velocity of the air.

Thirdly, Suppose the surface AC equal to AC no longer to be perpendicular to the stream of air, but inclined to it in the angle ACD, which we shall call the angle of incidence; then, by the resolution of forces, it follows, that the action of each particle is diminished in the proportion of radius to the sine of the angle of incidence, or of AC to AL, AL being perpendicular to CD.

Again: Draw AK parallel to CD. It is plain that no air lying farther from CD than KA is will strike the plane. The quantity of impulse therefore is diminished still farther in the proportion of AC to KC, or of AC to AL. Therefore, on the whole, the absolute impulse is diminished in the proportion of AC² to AL²; hence the proposition, that the impulse and resistance of a given surface are in the proportion of the square of the sine of the angle of incidence.

Fourthly, This impulse is in the direction PL, perpendicular to the impelled surface, and the surface tends to move in this direction; but suppose it moveable only in some other direction PO that we wish to employ this impulse, its action is therefore oblique; and if we wish to know the intensity of the impulse in this direction, it must be diminished still farther in the proportion of radius to the cosine of the angle LPO or sine of CPO. Hence the general proposition: The effective impulse is as the surface, as the square of the velocity of the wind, as the square of the sine of the angle of velocity of incidence, and as the sine of the obliquity jointly, which we may express by the symbol $R = S \cdot V^2 \cdot \sin^2 \theta \cdot \sin \phi$. And as the impulse depends on the density of the impelling fluid, we may take in every circumstance by the equation $R = S \cdot D \cdot V^2 \cdot \sin^2 \theta \cdot \sin \phi$.

It evidently follows from these premises, that if ACA' be a wedge, of which the base AA' is perpendicular to the wind, and the angle ACA' bisected by its direction, the direct or perpendicular impulse on the base is to the oblique impulse on the sides as radius to the square of the sine of half the angle ACA'.

The same must be affirmed of a pyramid or cone ACA', of which the axis is in the direction of the wind.

If ACA' (fig. 79) represent the section of a solid, produced by the revolution of a curve line APC round the axis CD, which lies in the direction of the wind, the impulse on this body may be compared with the direct impulse on this base, or the resistance to the motion of this body through the air may be compared with the direct resistance of its base, by resolving its surface into elementary planes PP, which are coincident with a tangent plane PR, and comparing the impulse on PP with the direct impulse on the corresponding part K k of the base.

In this way it follows that the impulse on a sphere is one half of the impulse on its great circle, or on the base of a cylinder of equal diameter.

We shall conclude this sketch of the doctrine with a very important proposition to determine the most advantageous position of a plane surface, when required to move in one direction while it is impelled by the wind blowing in a different direction. Thus:

Let AB (fig. 80) be the sail of a ship, CA the direction in which the wind blows, and AD the line of the ship's course. It is required to place the yard AC in such a position that the impulse of the wind upon the sail may have the greatest effect possible in impelling the ship along AD.

Let the points B, b, continually approach and ultimately coincide; the chord b B will ultimately coincide with a straight line CBD touching the circle in B; the triangles CDE, Cb e are similar, as also the triangles DBF, D b f; therefore BE² : b e² = BC² : b C², and BF : b f = BD : b D; and BE² × BF : b e² × b f = CB² × BD : C b² × b D. Therefore when AB is in the best position, so that BE² × BF is greater than b e² × b f, we shall have CB × BD greater than C b² × b D, or CB² × BD is also a maximum. This we know to be the case when CB = 2BD; therefore the sail must be so placed that the tangent of the angle of incidence shall be double of the tangent of the angle of the sail and keel.

In a common windmill the angle CAD is necessarily a right angle; for the sail moves in a circle to which the wind is perpendicular; therefore the best angle of the sail and axle will be 54° 44' nearly. Such is the theory of the resistance and impulse of the air. It is extremely simple and of easy application. In all physical theories there are assumptions which depend on other principles, and those on the judgment of the naturalist; so that it is always proper to confront the theory with experiment. There are even circumstances in the present case which have not been attended to in the theory. When a stream of air is obstructed by a solid body, or when a solid body moves along in air, the air is condensed before it and rarefied behind. There is therefore a pressure on the anterior parts arising from this want of equilibrium in the elasticity of the air. This must be superadded to the force arising from the impetus or inertia of the air. We cannot tell with precision what may be the amount of this condensation; it depends on the velocity with which any condensation diffuses itself. Also, if the motion be so rapid that the pressure of the atmosphere cannot make the air immediately occupy the place quitted by the body, it will sustain this pressure on its fore part to be added to the other forces.

Experiments on this subject are by no means numerous; at least such experiments as can be depended on for the foundation of any practical application. The first that have this character are those published by Mr. Robins in 1742, in his Treatise on Gunnery. They were repeated with some additions by the Chevalier Borda, and some account of them published in the Memoirs of the Academy of Sciences in 1763. In the Philosophical Transactions of the Royal Society of London, vol. lxiii., there are some experiments of the same kind on a larger scale by Mr. Edgeworth. These were all made in the way described in our account of Mr. Robins's improvements in gunnery. Bodies were made to move with determined velocities, and the resistances were measured by weights. In all these experiments the resistances were found very exactly in the proportion of the squares of the velocities; but they were found considerably greater than the weight of the column of air, whose height would produce the velocity in a falling body. Mr. Robins's experiments on a square of 16 inches, describing 25.2 feet per second, indicate the resistance to be to this weight nearly as 4 to 3. Borda's experiments on the same surface state the disproportion still greater.

The resistances are found not to be in the proportion of the surfaces, but increase considerably faster. Surfaces of 9, 16, 36, and 81 inches, moving with one velocity, had resistances in the proportion of 9, 17½, 42¾, and 104¾.

Now as this deviation from the proportion of the surfaces increases with great regularity, it is most probable that it continues to increase in surfaces of still greater extent; and these are the most generally to be met with in practice in the action of wind on ships and mills.

Borda's experiments on 81 inches show that the impulse of wind moving one foot per second is about \( \frac{1}{10} \) of a pound on a square foot. Therefore to find the impulse on a foot corresponding to any velocity, divide the square of the velocity by 500, and we obtain the impulse in pounds. Mr. Rouse of Leicestershire made many experiments, which are mentioned with great approbation by Mr. Smerton. His great sagacity and experience in the erection of windmills, oblige us to pay a considerable deference to his judgment. These experiments confirm our opinion, that the impulses increase faster than the surfaces. The following table was calculated from Mr. Rouse's observations, and may be considered as pretty near the truth:

| Velocity in feet | Impulse on a foot in pounds | |-----------------|----------------------------| | 0 | 0,000 | | 10 | 0,229 | | 20 | 0,915 |

| Velocity in feet | Impulse on a foot in pounds | |-----------------|----------------------------| | 30 | 2,059 | | 40 | 3,660 | | 50 | 5,718 |

If we multiply the square of the velocity in feet by 16, the product will be the impulse or resistance on a square foot in grains, according to Mr. Rouse's numbers.

The greatest deviation from the theory occurs in the oblique impulses. Mr. Robbins compared the resistance of a wedge, whose angle was 90°, with the resistance of its base; and instead of finding it less in the proportion of \( \sqrt{2} : 1 \), as determined by the theory, he found it greater in the proportion of 55 to 68 nearly; and when he formed the body into a pyramid, of which the sides had the same surface and the same inclination as the sides of the wedge, the resistance of the base and face were now as 55 to 39 nearly; so that here the same surface with the same inclination had its resistance reduced from 68 to 39 by being put into this form. Similar deviations occur in the experiments of the Chevalier Borda; and it may be collected from both, that the resistances diminish more nearly in the proportion of the sines of incidence than in the proportion of the squares of those sines.

The irregularity in the resistance of curved surfaces is as great as in plane surfaces. In general, the theory gives the oblique impulses on plane surfaces much too small, and the impulses on curved surfaces too great. The resistance of a sphere does not exceed the fourth part of the resistance of its great circle, instead of being its half; but the anomaly is such as to leave hardly any room for calculation. It would be very desirable to have the experiments on this subject repeated in a greater variety of cases, and on larger surfaces, so that the errors of the experiments may be of less consequence. Till this matter is reduced to some rule, the art of working ships must remain very imperfect, as must also the construction of windmills.

The case in which we are most interested in the knowledge of the resistance of the air is the motion of bullets and shells. Writers on artillery have long been sensible in the importance of the great effect of the air's resistance. It seems to have been this consideration that chiefly engaged Sir Isaac Newton to consider the motion of bodies in a resisting medium. A proposition or two would have sufficed for showing the incompatibility of the planetary motions with the supposition that the celestial spaces were filled with a fluid matter; but he has with great solicitude considered the motion of a body projected on the surface of the earth, and its deviation from the parabolic track assigned by Galileo. He has bestowed more pains on this problem than any other in his whole work; and his investigation has pointed out almost all the improvements which have been made in the application of mathematical knowledge to the study of nature. Nowhere does his sagacity and fertility of resource appear in so strong a light as in the second book of the Principia, which is almost wholly occupied by this problem. The celebrated mathematician John Bernoulli engaged in it as the finest opportunity of displaying his superiority. A mistake committed by Newton in his attempt to a solution was matter of triumph to him; and the whole of his performance, though a piece of elegant and elaborate geometry, is greatly hurt by his continually bringing this mistake, which is a mere trifle, into view. The difficulty of the subject is so great, that subsequent mathematicians seem to have kept aloof from it; and it has been entirely overlooked by the many voluminous writers who have treated professedly on military projectiles. They have supposed that the resistance of air was not so great as to render their theories erro-

Undulation neous; but as this will be found discussed under the article of air. Gunserly, nothing more shall be said of it here.

There is another motion of which air and other elastic fluids are susceptible, viz. an internal vibration of their particles, or undulation, by which any extended portion of air is distributed into alternate parcels of condensed and rarefied air, which are continually changing their condition without changing their places. By this change the condensation which is produced in one part of the air is gradually transferred along the mass of air to the greatest distances in all directions. It is of importance to have some distinct conception of this motion. It is found to be by this means that distant bodies produce in us the sensation of sound. Sir Isaac Newton treated this subject with his accustomed ingenuity, and has given us a theory of it in the end of the second book of his Principia. This theory has been objected to with respect to the conduct of the argument, and other explanations have been given by the most eminent mathematicians. Though they appear to differ from Newton's, their results are precisely the same; but, on a close examination, they differ no more than John Bernoulli's theorem of centripetal forces differs from Newton's, viz. the one being expressed by geometry and the other by literal analysis. The celebrated Lagrange reduces Newton's investigation to a tautological proposition or identical equation; but Dr M. Young of Trinity College, Dublin, has by a different turn of expression, freed Newton's method from this objection.

But since Newton published this theory of aerial undulations, and of their propagation along the air, and since the theory has been so corrected and improved as to be received by the most accurate philosophers as a branch of natural philosophy susceptible of rigid demonstration, it has been freely resorted to by many writers on other parts of natural science, who did not profess to be mathematicians, but made use of it for explaining phenomena in their own line on the authority of the mathematicians themselves. Learning from them that this vibration, and the quaquaverum propagation of the pulses, were the necessary properties of an elastic fluid, and that the rapidity of this propagation had a certain assignable proportion to the elasticity and density of the fluid, they freely made use of these concessions, and have introduced elastic vibrating fluids into many facts, where others would suspect no such thing, and have attempted to explain by their means many abstract phenomena of nature. Ethers are everywhere introduced, endowed with great elasticity and tenacity. Vibrations and pulses are supposed in this ether, and these are offered as explanations. The doctrines of animal spirits and nervous fluids, and the whole mechanical system of Hartley, by which the operations of the soul are said to be explained, have their foundation in this theory of aerial undulations. If these fancied fluids, and their internal vibrations, really operate in the phenomena ascribed to them, any explanation that can be given of the phenomena from this principle must be nothing else than showing that the legitimate consequences of these undulations are similar to the phenomena; or, if we are no more able to see this last step than in the case of sound, (which we know to be one consequence of the aerial undulations, although we cannot tell how), we must be able to point out, as in the case of sound, certain constant relations between the general laws of these undulations and the general laws of the phenomena. It is only in this way that we think ourselves entitled to say that the aerial undulations are causes, though not the only causes, of sound; and it is because there is no such relation, but, on the contrary, a total dissimilarity, to be observed between the laws of elastic undulations and the laws of the propagation of light, that we assert with confidence that ethereal undulations are not the causes of vision.

Explanations of this kind suppose, therefore, in the first place, that the philosopher who proposes them understands Undulation precisely the nature of these undulations; in the next place, that he makes his reader sensible of those circumstances of them which are concerned in the effect to be explained; and, in the third place, that he makes the reader understand how this circumstance of the vibrating fluid is connected with the phenomenon, either by showing it to be its mechanical cause, as when the philosopher explains the resounding of a musical chord to a flute or pipe which gave the same tone; or by showing that this circumstance of the undulation always accompanies the phenomenon, as when the philosopher shows that 238 vibrations of air in a second, in whatever manner or by whatever cause they are produced, always are followed by the sensation of the tone C in the middle of the harpsichord.

We propose now to give some account of the motion of elastic fluids; and the first thing incumbent on us is to show how these fluids differ from the unelastic in the propagation of any agitation of their parts. When a long tube is filled with water, and any one part of it pushed out of its place, the whole is instantly moved like a solid mass. But this is not the case with air. If a door be suddenly shut, the window at the farther end of a long and close room will rattle; but some time will elapse between the shutting of the door and the motion of the window. If some light dust be lying on a braced drum, and another be violently beat at a little distance from it, an attentive observer will see the dust dance up from the parchment; but this will be at the instant he hears the sound of the stroke on the other drum, and a sensible time after the stroke. Many such familiar facts show that the agitation is gradually communicated along the air; and therefore that when one particle is agitated by any sensible motion, a finite time, however small, must elapse before the adjoining particle is agitated in the same manner. This would not be the case in water if water be perfectly incompressible. We think that this may be made intelligible with very little trouble.

Let A, B, C, D, &c. be a row of aerial particles, at such distances that their elasticity just balances the pressure of the atmosphere; and let us suppose (as is deducible from the observed density of air being proportional to the compressing force) that the elasticity of the particles, by which they keep each other at a distance, is as their distances inversely. Let us farther suppose that the particle A has been carried, with an uniform motion, to a by some external force. It is evident that B cannot remain in its present state; for being now nearer to a than to C, it is propelled towards C by the excess of the elasticity of A above the natural elasticity of C. Let E be the natural elasticity of the particles, or the force corresponding to the distance BC or BA, and let F be the force which impels B towards C, and let f be the force exerted by A when at a. We have

\[ E : f = Ba : BC = Ba : BA \]

and

\[ E : f = Ba : BA = Ba : Ba : La \]

or

\[ E : f = Ba : La \]

Now, in fig. 81, let ABC be the line joining three particles, to which draw FG, PH parallel, and IAF, HBG perpendicular. Take IF or HG to represent the elasticity corresponding to the distance AB. Let the particle A be supposed to have been carried with an uniform motion to a by some external force, and draw RaM perpendicular to RG; and make FI : RM = Ba : BA. We shall then have FI : PM = Ba : La; and PM will represent the force... Undulation with which the particle B is urged towards C. Suppose this construction to be made for every point of the line AB, and that a point M is thus determined for each of them, mathematicians know that all these points M lie in the curve of a hyperbola, of which FG and GH are the asymptotes. It is also known by the elements of mechanics, that since the motion of A along AB is uniform, AA or IP may be taken to represent the time of describing AA; and that the area IPM represents the whole velocity which B has acquired in its motion towards C when A has come to a, the force urging B being always as the portion PM of the ordinate.

Take GX of any length in HG produced, and let GX represent the velocity which the uniform action of the natural elasticity IF could communicate to the particle B during the time that A would uniformly describe AB. Make GX to GY as the rectangle IFGH to the hyperbolic space IFRP, and draw YS cutting MR produced in S, and draw FX cutting MR in T. It is known to the mathematicians that the point S is in a curve line FSs, called the logarithmic curve; of which the leading property is, that any line RS parallel to GX is to GX as the rectangle IFGH is to the hyperbolic space IFRP, and that FX touches the curve in F.

This being the case, it is plain, that because RT increases in the same proportion with FR, or with the rectangle IFRP, and RS increases in the proportion of the space IFRP, TS increases in the proportion of the space IPM. Therefore TS is proportional to the velocity of B when A has reached a, and RT is proportional to the velocity which the uniform action of the natural elasticity would communicate to B in the same time. Then since FT is as the time, and TS is as the velocity, the area RTS will be as the space described by B, urged by the variable force PM; while A, urged by the external force, describes AA; and the triangle FRT will represent the space which the uniform action of the natural elasticity would cause B to describe in the same time.

And thus it is plain that these three motions can be compared together: the uniform motion of the agitated particle A, the uniformly accelerated motion which the natural elasticity would communicate to B by its constant action, and the motion produced in B by the agitation of A. But this comparison, requiring the quadrature of the hyperbola and logarithmic curve, would lead us into most intricate and tedious computations. Of these we need only give the result, and make some other comparisons which are palpable.

Let AA be supposed indefinitely small in comparison of AB. The space described by A is therefore indefinitely small; but in this case we know that the ratio of the space FRT to the rectangle IFRP is indefinitely small. There is therefore no comparison between the agitation of A by the external force, and the agitation which natural elasticity would produce on a single particle in the same time, the last being incomparably smaller than the first. And this space FRT is incomparably greater than FTS; and therefore the space which B would describe by the uniform action of the natural elasticity is incomparably greater than what it would describe in consequence of the agitation of A.

From this reasoning we see evidently that A must be sensibly moved, or a finite or measurable time must elapse before B acquires a measurable motion. In like manner, B must move during a measurable time before C acquires a measurable motion, &c.; and therefore the agitation of A is communicated to the distant particles in gradual succession.

By a further comparison of these spaces we learn the time in which each succeeding particle acquires the very agitation of A. If the particles B and C only are considered, and the motion of C neglected, it will be found that B has acquired the motion of A a little before it has described one-third of the space described by A; but if the undulation of C be considered, the acceleration of B must be increased by the retreat of C, and B must describe a greater space in proportion to that described by A. By computation it appears, that when both B and C have acquired the velocity of A, B has described nearly one-half of A's motion, and C more nearly one-third. Extending this to D, we shall find that D has described still more nearly one-fourth of A's motion. And from the nature of the computation it appears that this approximation goes on rapidly; therefore, supposing it accurate from the very first particle, it follows from the equable motion of A, that each succeeding particle moves through an equal space in acquiring the motion of A.

The conclusion which we must draw from all this is, that when the agitation of A has been fully communicated to a particle at a sensible distance, the intervening particles, all moving forward with a common velocity, are equally compressed as to sense, except a very few of the first particles; and that this communication, or this propagation of the original agitation, goes on with an uniform velocity.

These computations need not be attended to by such as do not wish for an accurate knowledge of the precise agitation of each particle. It is enough for such readers to see clearly that time must escape between the agitation of A and that of a distant particle; and this is abundantly manifest from the incomparability (excuse the term) of the nascent rectangle IFRP with the nascent triangle FRT, and the incomparability of FRT with FTS.

What has now been shown of the communication of any Newton's sensible motion A a must hold equally with respect to any demonstration of this motion. Therefore if a tremendous motion of air on this body, such as a spring or bell, should agitate the adjoining subjecting particle A by pushing it forward in the direction AB, and then allowing it to come back again in the direction BA, an agitation similar to this will take place in all the particles of the row one after the other. Now if this body vibrate according to the law of motion of a pendulum vibrating in a cycloid, the neighbouring particle of air will of necessity vibrate in the same manner; and then Newton's demonstration in the article Acoustics needs no apology. Its only deficiency was, that it seemed to prove that this would be the way in which every particle would of necessity vibrate; which is not true, for the successive parcels of air will be differently agitated according to the original agitation. Newton only wants to prove the uniform propagation of the agitations, and he selects that form which renders the proof easiest. He proves, in the most unexceptionable manner, that if the particles of a pulse of air are really moving like a cycloidal pendulum, the forces acting on each particle, in consequence of the compression and dilatation of the different parts of the pulse, are precisely such as are necessary for continuing this motion, and therefore no other forces are required. Then since each particle in a certain part of its path, is moving in a certain direction, and with a certain velocity, and urged by a determined force, it must move in that very manner. The objection started by John Bernoulli against Newton's demonstration of the elliptical motion of a body urged by a force in the inverse duplicate ratio of the distance from the focus, is precisely the same with the objection against Newton's demonstration of the progress of aerial undulations, and is equally futile.

It must, however, be observed, that Newton's demonstration proceeds on the supposition that the linear agitations of a particle are incomparably smaller than the extent of an undulation. This is not strictly the case in any instance, and in many it is far from being true. In a pretty strong twang of a harpsichord wire, the agitation of a particle may be near the 50th part of the extent of the undulation. This must disturb the regularity of the motion, and cause the Undulation agitations in the remote undulations to differ from those of air in the first pulse. In the explosion of a cannon, the breaking of an exhausted bottle, and many instances which may be given, the agitations are still greater. The commentators on Newton's Principia, Le Sueur and Jacquier, have shown, and Euler more clearly, that when the original agitations are very violent, the particles of air will acquire a subordinate vibration compounded with the regular cycloidal vibration, and the progress of the pulses will be somewhat more rapid; but the intricacy of the calculus is so great, that they have not been able to determine with any tolerable precision what the change of velocity will be.

All this, however, is fully confirmed by experiment on sounds. The sound of a cannon at 10 or 20 miles distance does not in the least resemble its sound when near. In this case it is a loud instantaneous crack, to which we can assign no musical pitch. At a distance, it is a grave sound, of which we can tell the note; and it begins softly, swells to its greatest loudness, and then dies away growling. The same may be said of a clap of thunder, which we know to be a loud snap of still less duration. It is highly probable that the appreciable tones which those distant sounds afford are produced by the continuance of these subordinate vibrations which are added together and fortified in the successive pulses, though not perceptible in the first, in a way somewhat resembling the resonance of a musical chord. Newton's explanation gathers evidence therefore from this circumstance. And we must further observe, that all elastic bodies tremble or vibrate almost precisely as a pendulum swinging in a cycloid, unless their vibrations are uncommonly violent; in which case they are quickly reduced to a moderate quantity by the resistance of the air. The only very loud sounds which we can produce in this way are from great bells; and in these the utmost extent of the vibration is very small in comparison with the breadth of the pulse. The velocity of these sounds has not been compared with that of cannon, or perhaps it would be found less, and an objection against Newton's determination removed. He gives 969 feet per second, (experiment 1142.)

But it is also very probable, that in the propagation through the air, the agitation gradually and rapidly approaches to this regular cycloidal form in the successive pulses, in the same way as we observe that whatever is the form of agitation in the middle of a smooth pond of water, the spreading circles are always of one gentle form without asperities. In like manner, into whatever form we throw a stretched cord by the twang which we give it, it almost immediately makes smooth undulations, keeping itself in the shape of an elongated trochoid. Of this last we can demonstrate the necessity, because the case is simple. In the wave, the investigation is next to impossible; but we see the fact. We may therefore presume it in air. And accordingly we know that any noise, however abrupt and jarring near at hand, is smooth at a distance. Nothing is more rough and harsh than the scream of a heron; but at half a mile's distance it is soft. The ruffle of a drum is also smooth at a distance.

Fig. 82 shows the successive situations of the particles of a row. Each line of the figure shows the same particles marked with the same letters; the first particle \(a\) being supposed to be removed successively from its quiescent situation and back to it again. The mark \(X\) is put on that part of each line where the agitated particles are at their natural distances, and the air is of the natural density. The mark \(I\) is put where the air is most of all compressed, and \(J\) where it is most of all dilated; the curve line drawn through the lowest line of the figure is intended to represent the density in every point, by drawing ordinates to it from the straight line. The ordinates below the line indicate a rarity, and those above the line a density, greater than common. It appears that when \(a\) has come back to its natural situation, the part of greatest density is between the particles \(f\) and \(k\), and the greatest rarity between \(c\) and \(d\).

We have only to add, that the velocity of this propagation depends on the elasticity and density of the fluid. If these vary in the same proportion, that is, if the fluid has its elasticity proportional to its density, the velocity will remain the same. If the elasticity or density alone be changed, the velocity of the undulations will change in the direct sub-duplicate ratio of the elasticity and the inverse subduplicate ratio of the density; or should the elasticity be quadrupled, the quantity of motion produced by it in any given time will be quadrupled. This will be the case if the velocity be doubled; for there would then be double the number of particles doubly agitated. Should the density be quadrupled, the elasticity remaining the same, the quantity of motion must remain the same. This will be the case if the velocity be reduced to one half; for this will propagate half the agitation to half the distance, which will communicate it to twice the number of particles, and the quantity of motion will remain the same. The same may be said of other proportions, and therefore \(V = \frac{\sqrt{E}}{\sqrt{D}}\). Therefore a change in the barometer will not affect the velocity of the undulations in air; but they will be accelerated by heat, which diminishes its density, or increases its elasticity. The velocity of the pulses in inflammable air must be at least thrice as great, because its density is but one-tenth of that of air when the elasticity of both are the same.

Let us now attend a little to the propagation of aerial further pulses as they really happen; for this hypothesis of a single consideration of a row of particles is nowhere to be observed. Suppose a vessel which contains it is suddenly annihilated. The air must expand to its natural dimensions, suppose BCD. But it cannot do this without pressing aside the surrounding air. We have seen that in any single row of particles this cannot be at once diffused to a distance, but must produce a condensation in the air adjoining; which will be gradually propagated to a distance. Therefore this sphere BCD of the common density will form round it a shell, bounded by EFG, of condensed air. Suppose that at this instant the inner air BCD becomes solid. The shell of condensed air can expand only outwards. Let it expand till it is of the common density, occupying the shell HIK. This expansion must, in like manner, produce a shell of condensed air without it; and at this instant let HIK become solid. The surrounding shell of condensed air can expand only outward, condensing another shell without it. It is plain that this must go on continually, and the central agitation will be gradually propagated to a distance in all directions. But, in this process, it is not the same numerical particles that go to a distance. Those of the original Undulation sphere go no further than BCD, those of the next shall go no further than HIK, &c. Further, the expansion outwards of any particle will be more moderate as the diffusion advances; for the whole motion of each shell cannot exceed the original quantity of motion; and the number of particles in each successive shell increases as the surface, that is, as the square of the distance from the centre; therefore the agitation of the particles will decrease in the same ratio, or will be in the inverse duplicate ratio of the distance from the centre. Each successive shell, therefore, contains the same quantity of motion, and the successive agitations of the particles of any row out from the centre will not be equal to the original agitation, as happens in the solitary row. But this does not affect the velocity of the propagation, because all agitations are propagated equally fast.

We supposed the air A to become solid as soon as it acquired the common density; but this was to facilitate the conception of the diffusion. It does not stop at this bulk; for while it was denser it had a tendency to expand. Therefore each particle has attained this distance with an accelerated motion. It will, therefore, continue this motion like a pendulum that has passed the perpendicular, till it is brought to rest by the air without it; and it is now rarer than common air, and collapses again by the greater elasticity of the air without it. This outward air, therefore, in regaining its natural density, must expand both ways. It expands towards the centre, following the collapsing of the air within it; and it expands outwards, condensing the air beyond it. By expanding inwards, it will again condense the air within it, and this will again expand; a similar motion happens in all the outward shells; and thus there is propagated a succession of condensed and rarefied shells of air, which gradually swell to the greatest distance.

It may be demonstrated, that when the central air has for the second time acquired the natural density, it will be fact of drop at rest, and be disturbed no more; and that this will happen ping a pebble into all the shells in succession. But the demonstration is much too intricate for this place; and we must be contented with pointing out a fact perfectly analogous. When we drop a small pebble into water, we see it produce a series of circular waves, which go along the surface of smooth water to a great distance, becoming more and more gentle as they recede from the centre; and the middle, where the agitation was first produced, remains perfectly smooth, and this smoothness extends continually; that is, each wave when brought to a level remains at rest. Now these waves are produced and propagated by the depression and elevation made at the centre. The elevation tends to diffuse itself; and the force with which each particle of water is actuated is a force acting directly up and down, and is proportional to the elevation or depression of the particle. This hydrostistical pressure operates precisely in the same way as the condensation and rarefaction of the air; and the mathematical investigation of the propagation of the circular undulations on smooth water is similar in every step to that of the propagation of the spherical waves in still air. For this we appeal to Newton's Principia, or to Euler's Opuscula, where he gives a very beautiful investigation of the velocity of the aerial pulses; and to some memoirs of Lagrange in the collections of the academies of Berlin and Turin. These two last authors have made the investigation as simple as seems possible, and have freed it from every objection which can be stated against the geometrical one of their greater teacher Newton.

Having said this much respecting the similarity between the waves on water and the aerial undulations, we shall have recourse to them, as affording us a very sensible object to represent many affections of the other which it would be extremely difficult to explain. We neither see nor feel the aerial undulations; and they behoved, therefore, to be described very abstractedly and imperfectly. In the watery wave there is no permanent progressive motion of the water from the centre. Throw a small bit of cork on the surface, and it will be observed to pop up and down without the least motion outwards. In like manner, the particles of air are only agitated a very little outwards and inwards, which motion is communicated to the particles beyond them, whilst they themselves come to rest; unless agitated afresh; and this agitation of the particles is inconceivably small. Even the explosion of a cannon at no great distance will but gently agitate a feather, giving it a single impulse outwards, and immediately after another inwards or towards the cannon. When a harpsichord wire is forcibly twanged at a few feet distance, the agitation of the air is next to insensible. It is not, however, nothing; and it differs from that in a watery wave by being really outwards and inwards. In consequence of this, when the condensed shell reaches an elastic body, it impels it slightly. If its elasticity be such as to make it acquire the opposite shape at the instant that the next agitation and condensed shell of air touches it, its agitation will be doubled, and a third agitation will increase it, and so on, till it acquire the agitation competent to that of the shell of air which reaches it, and it is thrown into sensible vibration, and gives a sound extremely faint indeed, because the agitation which it acquires is that corresponding to a shell of air considerably removed from the original string. Hence it happens that a musical chord, pipe, or bell, will cause another to resound, whose vibrations are isochronous with its own; or if the vibrations of the one coincides with every second, or third, or fourth, &c. of the other; just as we can put a very heavy pendulum into sensible motion by giving it a gentle push with the breath at every vibration, or at every second, third, or fourth, &c. A drum struck in the neighbourhood of another drum will agitate it very sensibly; for here the stroke depresses a very considerable surface, and produces an agitation of a considerable mass of air; it will even agitate the surface of stagnant water. The explosion of a cannon will even break a neighbouring window. The shell of condensed air which comes against the glass has a great surface and a great agitation; the best security in this case is to throw up the sash; this admits the condensed air into the room, which acts on the inside of the window, balancing part of the external impulse.

It is demonstrated in every elementary treatise of natural philosophy, that when a wave on water meets any plane air and obstacle, it is reflected by it from a centre equally removed behind the obstacle; that waves radiating from the focus of a parabola are reflected in waves perpendicular to its axis; that waves radiating from one focus of an ellipse are made to converge to the other focus, &c. All this may be affirmed of the aerial undulations; that when part of a wave gets through a hole in the obstacle, it becomes the centre of a new series of a waves; that waves bend round the extremities of an obstacle; all this happens in the aerial undulations. And lastly, that when the surface of water is thrown into regular undulations by one agitation, another agitation in another place will produce other regular waves, which will cross the former without disturbing them in the smallest degree. The same thing happens in air; and experiments may be made on water which will illustrate in the most perfect manner many other affections of the aerial pulses, which we should otherwise conceive very imperfectly. We would recommend to our curious readers to make some of these experiments in a large vessel of milk. Take a long and narrow plate of lead, which, when set on the bottom of the vessel, will reach above the surface of the milk; bend this plate into a parabola, elliptical, or other curve. Make the undulations by dropping milk on the focus from a small pipe, which will cause the agitations to succeed with rapidity, and then all that we have said will be most distinctly seen, and the experiment will be Effects of very amusing and instructive, especially to the musical reader.

We shall now proceed to explain a number of natural appearances, depending on the pressure and the elasticity of the air; appearances not sufficiently general, or too complicated for the purposes of argument, whilst we were employed in the investigation of these properties, but too important to be passed over in silence.

It is owing to the pressure of the atmosphere that two surfaces which accurately fit each other cohere with such force. This is a fact familiarly known to the glass-grinders, polishers of marble, &c. A large lens or speculum, ground on its tool till it becomes very smooth, requires more than any man's strength to separate it directly from the tool. If the surface is only a square inch, it will require fifteen pounds to separate them perpendicularly, though a very moderate force will make them slide along each other. But this cohesion is not observed unless the surfaces are wetted or smeared with oil or grease; otherwise the air gets between them, and they separate without any trouble.

That this cohesion is owing to the atmospheric pressure, is evident from the ease with which the plates may be separated in an exhausted receiver. To the same cause we must ascribe the very strong adhesion of snails, periwinkles, limpets, and other univalve shells, to the rocks. The animal forms the rim of its shell, so as to fit the shape of the rock to which it intends to cling. It then fills its shell, if not already filled by its own body, with water. In this condition it is evident that we must act with a force equal to fifteen pounds for every square inch of touching surface before we can detach it. This may be illustrated by filling a drinking-glass to the brim with water, and having covered it with a piece of thin wet leather, invert it on a table, and then try to pull it straight up; which will require a considerable force. But if we expose a small adhering to a stone in the exhausted receiver, we shall see it drop off by its own weight. In the same manner do the remora, the polypus, the lamprey, and many other animals, adhere with such firmness. Boys frequently amuse themselves by pulling out large stones from the pavement by means of a circle of stiff wetted leather fastened to a string. It is owing to the same cause that the bivalve shell fishes keep themselves so firmly shut. We think the muscular force of an oyster prodigious, because it requires such force to open it; but if we grind off a bit of the convex shell, so as to make a hole in it, though without hurting the fish in the smallest degree, it opens with great ease, as it does also in vacuo.

The pressure of the air, operating in this way, contributes much to the cohesion of bodies, where we do not suspect its influence. The tenacity of our mortars and cements would frequently be ineffectual without this assistance. It is owing to the pressure of the atmosphere that a cask will not run by the cock unless a hole be opened in some other part of the cask. If the cask is not quite full, some liquor indeed will run out, but it will stop as soon as the diminished elasticity of the air above the liquor is in equilibrium, together with the liquor, with the atmospheric pressure. In like manner, a teapot must have a small hole in its lid to ensure its pouring out the tea. If indeed the hole in the cask is of large dimensions, it will run without any other, because air will get in at the upper side of the hole while the liquor runs out by the lower part of it. On the same principle depends the performance of an instrument used by the spirit-dealers for taking out a sample of their spirits. It consists of a long thin plate tube AB (fig. 84.), open a-top at A, and ending in a small hole at B. The end B is dipped into the spirits, which rises into the tube; then the thumb is clasped on the mouth A, and the whole is lifted out of the cask. The spirit remains in it till the thumb be taken off; it is then allowed to run into a glass for examination.

It seems principally owing to the pressure of the air that frosts immediately occasion a scarcity of water in our fountains and wells. This is erroneously accounted for, by supposing that the water freezes in the bowels of the earth. But this is a great mistake. The most intense frost of a Siberian winter would not freeze the ground two feet deep; but a very moderate frost will consolidate the whole surface of a country, and make it impervious to the air; especially if the frost has been preceded by rain, which has soaked the surface. When this happens, the water which was filtering through the ground is all arrested and kept suspended in its capillary tubes by the pressure of the air, in the very same manner as the spirits are kept suspended in the instrument just now described by the thumb's shutting the hole A. A thaw melts the superficial ice, and allows the water to run in the same manner as the spirits run when the thumb is removed.

Common air is necessary for supporting the lives of most animals. If a small animal, such as a mouse or bird, be put into the receiver of an air-pump, and the air be exhausted, the animal will quickly be thrown into convulsions and fall down dead; if the air be immediately readmitted, the animal will sometimes revive, especially if the rarefaction has been briskly made, and has not been very great. We do not know that any breathing animal can bear the air to be reduced to one-fourth of its ordinary density, nor even one-third; nor have we good evidence that an animal will ever recover if the rarefaction is pushed very far, although continued for a very short time.

But the mere presence of the air is by no means sufficient for preserving the life of the animal; for it is found, that an animal shut up in a vessel of air cannot live in it for any length of time. If a man be shut up in a box containing a wine hogshead of air, he cannot live in it much above an hour, and long before this he will find his breathing very unsatisfactory and uneasy. A gallon of air will support him about a minute.

A box EF (fig. 85.) may be made, having a pipe AB inserted into its top, and fitted with a very light valve at B, opening upwards. This pipe sends off a lateral branch dD dC, which enters the box at the bottom, and is also fitted with a light valve at C opening upwards. If a person breathe through the pipe, keeping his nostrils shut, it is evident that the air which he expires will not enter the box by the hole B, nor return through the pipe CDd; and by this contrivance he will gradually employ the whole air of the box.

With this apparatus experiments can be made without any risk or inconvenience, and the quantity of air necessary for a given time of easy breathing may be accurately ascertained.

How the air of our atmosphere produces this effect is not a question for mechanical philosophy to determine. While a certain amount of atmospheric pressure and elasticity is necessary to balance the mechanical impulse of the blood, and to maintain a sufficient supply of air in the lungs; these play but a subordinate part to the subtle agency more immediately concerned in maintaining the animal functions. Quito in Peru, and the country round Gondar in Abyssinia, are so far elevated above the surface of the ocean, that the pressure and the elasticity of the air are one-third less Effects of the pressure of the air.

And, on the other hand, we know, that when an animal has breathed in any quantity of air for a certain time without renewal, it will not only be suffocated, but another animal put into this air will die immediately. And we do not find either the pressure or elasticity of the air remarkably diminished; it is indeed diminished, but by a very small quantity. Restoring the former pressure and elasticity has not the smallest tendency to prevent the death of the animal; for an animal will live no longer under a receiver that has its mouth inverted on water, than in one set upon the pump-plate covered with leather. Now when the receiver is set on water, the pressure of the atmosphere acts completely on the included air, and preserves it in the same state of elasticity.

In short, it is known that the air which has already served to maintain the animal functions has its chemical and alimentary properties completely changed, and is no longer fit for this purpose. So much of any mass of air as has really been thus employed is changed into what is called fixed air by Dr. Black, or carbonic acid by the chemists of the school of Lavoisier. Any person may be convinced of this by breathing or blowing through a pipe immersed in lime water. Every expiration will produce white clouds on the water, till all the lime which it contains is precipitated in the form of pure chalk. In this case we know that the lime has combined with the fixed air.

The celebrated Dr. Stephen Hales made many experiments, with a view to clear the air from the noxious vapour which he supposed to be emitted from the lungs. He made use of the apparatus which we have been just now mentioning; and he put several diaphragms ff, ff, &c. of thin woollen stuff into the box, and moistened them with various liquids. He found nothing so efficacious as a solution of potash. We now understand this perfectly. If the solution is not already saturated with fixed air, it will take it up as fast as it is produced, and this will purify the air: a solution of caustic alkali therefore will have this effect till it is rendered quite mild.

These experiments have been repeated, and varied in many circumstances, in order to ascertain whether this fixed air was really emitted by the lungs, or whether the inspired air was in part changed into fixed air by its combination with some other substance. This is a question which comes properly in our way, and which the doctrines of pneumatics enable us to answer. If the fixed air be emitted in substance from the lungs, it does not appear how a renewal of the air into which it is emitted is necessary, for this does not hinder the subsequent emission; and the bulk of the air would be increased by breathing in it, viz. by the bulk of all the fixed air emitted; but, on the contrary, it is a little diminished. We must therefore adopt the other opinion; and the discoveries in modern chemistry enable us to give a pretty accurate account of the whole process. Fixed air is acknowledged to be a compound, of which one ingredient is found to constitute nearly one-fourth of the whole atmospheric fluid, we mean vital air or the oxygen of Lavoisier. When this is combined with phlogiston, according to the doctrine of Stahl, or with carbon, according to Lavoisier, the result is fixed air or carbonic acid. The change therefore which breathing makes on the air is the solution of this matter by vital air; and the use of air in breathing is the carrying off this noxious principle in the way of solution. When therefore the air is already so far saturated as not to dissolve this substance as fast as it is secreted, or must be secreted in the lungs, the animal suffers the pain of suffocation, or is otherwise mortally affected. Suffocation is not the only consequence; for we can remain for a number of seconds without breathing, and then we begin to feel the true pain of suffocation; but those who have been instantaneously struck down by an inspiration of fixed air, and afterwards recovered to life, complained of no such pain, and seemed to have suffered chiefly by a nervous affection. It is said, but we will not vouch for the truth of it, that a person may safely take a full inspiration of fixed air, if the passages of the nose be shut; and that unless these nerves are stimulated by the fixed air, it is not instantaneously mortal. But these are questions out of our present line of inquiry. They belong to physiology, and are treated of in other places of this work. Our business is to explain in what manner the pressure and elasticity of the air, combined with the structure and mechanism of the body, operate in producing this necessary secretion and removal of the matter discharged from the lungs in the act of breathing.

It is well ascertained, that the secretion is made from the mass of blood during its passage through the lungs. The blood delivered into the lungs is of a dark blackish colour, and is there changed into a florid red. In the lungs it is exposed to the action of the air in a prodigiously extended surface; for the lungs consist of an inconceivable number of small vessels or bladders, communicating with each other and with the windpipe. These are filled with air in every inspiration. Those vessels are everywhere in contact with minute blood-vessels. The blood does not in toto come into immediate contact with the air; and it would seem that it is only the thin serous part of it which is acted on by the air at the mouths of the vessels or pores, where it stands by capillary attraction. Dr. Priestley found, that venous blood inclosed in thin bladders and other membranes was rendered florid by keeping the bladders in contact with abundance of pure vital air. We know also, that breath is moist or damp, and must have acquired this moisture in the lungs. It is immaterial whether this secretion of water or lymph, as the anatomists call it, be furnished by mere exudation through simple pores, or by a vascular and organic secretion; in either case, some ingredient of the blood comes in contact with air in the lungs, and there unites with it. This is farther confirmed, by observing, that all breathing animals are warmer than the surrounding medium, and that by every process in which fixed air is formed from vital air, heat is produced. Hence the formation of this gas by the union of atmospheric oxygen with carbon in the blood is generally assigned as the source of animal heat. We touch on these things in a very transitory way in this place, only to prove that, for the support of animal life, there must be a very extensive application of the air to the blood, and that this is made in the lungs.

The question under consideration here is, How is this brought about by the weight and elasticity of the air? The answer is, it is done in two ways; by the action of the muscles of the ribs, and by the action of the diaphragm and other muscles of the abdomen. The thorax or chest is a great cavity, completely filled by the lungs. The sides of this cavity are formed by the ribs. These are crooked or arched, and each is moveable round its two ends, one of them being inserted into the vertebra of the back, and the other into the sternum or breast-bone. The rib turns in a manner resembling the handle of a drawer.

The inspection of fig. 86 will illustrate this matter a little. Suppose the curves a c e, b k f, c l g, &c. to represent the ribs moveable round the extremities. Each succeeding rib is more bent than the one above it; and this curvature is both in the vertical and horizontal direction. Suppose each so broad as to project a little over its inferior like the tiles of a roof. It is evident, that if we take the lower one by its middle, and draw it out a little, moving it round the line n p, it will bring out the next d m h along with it. Also, because the dis- Effects of tance of the middle point \(a\) from the axis of motion \(mp\) is greater than the distance of \(m\) from the axis \(dh\), and because \(o\) will therefore describe a portion of a larger circle than \(m\) does, the rib \(mp\) will slide up a little under the rib \(dh\), or the rib \(dh\) will overlap \(mp\) a little more than before; the distance \(om\) will therefore be diminished. The same must happen to all the superior ribs; but the change of distance will be less and less as we go upwards. Now, instead of this great breadth of the ribs overlapping each other, suppose each inferior rib connected with the one above it by threads or fibres susceptible of contraction at the will of man. The articulations \(e, a\) of the first or upper rib with the spine and sternum are so broad and firm, that this rib can have little or no motion round the line \(ae\); this rib therefore is as a fixture for the ends of all the contracting fibres; therefore, whenever the fibres which connect the second rib with the first rib contract, the second must rise a little, and also go outward, and will carry the lower ribs along with it; the third rib will still rise farther by the contraction of the muscles which connect it with the second, and so on; and thus the whole ribs are raised and thrown outward (and a little forward, because the articulation of each with the spine is considerably higher than that with the sternum), and the capacity of the thorax is enlarged by the contraction of its muscular covering. The direction of the muscular fibres is very oblique to the direction of the circular motion which it produces; from which circumstance it follows, that a very minute contraction of the muscles produces all the motion which is necessary. This indeed is not great; the whole motion of the lowest ribs is less than an inch in the most violent inspiration, and the whole contraction of the muscles of the twelve ribs does not exceed the eighth part of an inch, even supposing the intercostal muscles at right angles to the ribs; and being oblique, the contraction is still less. It would seem, that the intensity of the contractive power of a muscular fibre is easily obtained, but that the space through which it can be exerted is very limited; for in most cases nature places the muscles in situations of great mechanical disadvantage in this respect, in order to procure other conveniences.

But this is not the whole effect of the contraction of the intercostal muscles; since the compound action of the two sets of muscles, which cross each other from rib to rib like the letter X, is nearly at right angles to the rib, but is oblique to its plane, it tends to push the ribs closer on their articulations, and thus to press out the two pillars on which they are articulated. Thus, supposing \(af\) (fig. 87) to represent the section of one of the vertebrae of the spine, and \(cd\) a section of the sternum, and \(ab, ef, cd\) opposite ribs, with a lax thread \(be\) connecting them. If this thread be pulled upwards by the middle \(g\) till it is tight, it will tend to pull the points \(b\) and \(e\) nearer to each other, and to press the vertebra \(af\) and the sternum \(cd\) outwards. The spine being the chief pillar of the body, may be considered as immovable in the present instance. The sternum is sufficiently susceptible of motion for the present purpose. It remains almost fixed a-top at its articulation with the first rib, but it gradually yields below; and thus the capacity of the thorax is enlarged in this direction also. The whole enlargement of the diameters of the thorax during inspiration is very small, not exceeding the fifth part of an inch in ordinary cases. This is easily calculated. Its quiescent capacity is about two cubic feet, and we never draw in more than fifteen inches. Two spheres, one of which holds two cubic feet and the other two feet and fifteen inches, will not differ in diameter above the fifth part of an inch.

The other method of enlarging the capacity of the thorax is very different. It is separated from the abdomen by a strong muscular partition called the diaphragm, which is attached to firm parts all around. In its quiescent or relaxed state it is considerably convex upwards, that is, towards the thorax, rising up into its cavity like the bottom of an ordinary quart bottle, only not so regular in its shape. Many of its fibres tend from its middle to the circumference, where they are inserted into firm parts of the body. Now suppose these fibres to contract. This must draw down its middle, or make it flatter than before, and thus enlarge the capacity of the thorax.

Physiologists are not well agreed as to the share which each of these actions has in the operation of enlarging the thorax. Many refuse all share of it to the intercostal muscles, and say that it is performed by the diaphragm alone. But the fact is, that the ribs are really observed to rise even while the person is asleep; and this cannot possibly be produced by the diaphragm, as these anatomists assert. Such an opinion shows either ignorance or neglect of the laws of pneumatics. If the capacity of the thorax were enlarged only by drawing down the diaphragm, the pressure of the air would compress the ribs, and make them descend. And the simple laws of mechanics make it as evident as any proposition in geometry, that the contraction of the intercostal muscles must produce an elevation of the ribs and enlargement of the thorax; and it is one of the most beautiful contrivances of nature. It depends much on the will of the animal what share each of these actions shall have. In general, the greatest part is done by the diaphragm; and any person can breathe in such a manner that his rib shall remain motionless; and, on the contrary, he can breathe almost entirely by raising his chest. In the first method of breathing, the belly rises during inspiration, because the contraction of the diaphragm compresses the upper part of the bowels, and therefore squeezes them outwards; so that an ignorant person would be apt to think that the breathing was performed by the belly, and that the belly is inflated with the air. The strait lacing of the women impedes the motion of the ribs, and changes the natural habit of breathing, or brings on an unnatural habit. When the mind is depressed, it is observed that the breathing is more performed by the muscles of the thorax; and a deep sigh is always made in this way.

These observations on the manner in which the capacity of the chest can be enlarged were necessary, before we can acquire a just notion of the way in which the mechanical properties of air operate in applying it to the mass of blood during its passage through the lungs. Suppose the thorax quite empty, and communicating with the external air by means of the trachea or windpipe, it would then resemble a pair of bellows. Raising the boards corresponds to the raising of the ribs; and we might imitate the action of the diaphragm by forcibly pulling outwards the folded leather which unites them. Thus their capacity is enlarged, and the air rushes in at the nozzle by its weight in the same manner as water would do. The thorax differs from bellows only in this respect, that it is filled by the lungs, which is a vast collection of little bladders, like the holes in a piece of fermented bread, all communicating with the trachea, and many of them with each other. When the chest is enlarged, the air rushes into them all in the same manner as into the single cavity of an empty thorax. It cannot be said with propriety that they are inflated; all that is done is allowing the air to come in. At the same time, as their membranous covering must have some thickness, however small, and some elasticity, it is not unlikely that, when compressed by expiration, they tend a little to recover their former shape, and thus aid the voluntary action of the muscles. It is in this manner that a small bladder of couthouse swells again after compression, and fills itself with air or water. But this cannot happen except in the most minute vesicles; those of sensible bulk have not elasticity.

Effects of enough for this purpose. The lungs of birds, however, have some very large bladders, which have a very considerable elasticity, and recover their shape and size with great force after compression, and thus fill themselves with air. The respiration of these animals is considerably different from that of land animals, and their muscles act chiefly in expiration. This will be explained by and by as a curious variety in the pneumatic instrument.

Air taken in, not by our own action, but by external pressure.

This account of the manner in which the lungs are filled with air does not seem agreeable to the notions we entertain of it. We seem to suck in the air; but although it be true that we act, and exert force, in order to get air into our lungs, it is not by our action, but by external pressure, that it does come in. If we apply our mouth to the top of a bottle filled with water, we find that no draught, as we call it, of our chest will suck in any of the water, but if we suck in the very same manner at the end of a pipe immersed in water, it follows immediately. Our interest in the thing makes us connect in imagination our own action with the effect, without thinking on the many steps which may intervene in the train of natural operations; and we consider the action as the immediate cause of the reception of the air into the lungs. It is as if we opened the door, and took in by the hand a person who was really pushed in by the crowd without. If an incision be made into the side of the thorax, so that the air can get in by that way, when the animal acts in the usual manner, the air will really come in by this hole, and fill the space between the lungs and the thorax; but no air is sucked into the lungs by this process, and the animal is as completely suffocated as if the windpipe were shut up. And, on the other hand, if a hole be made into the lungs without communicating with the thorax, the animal will breathe through this hole, though the windpipe be stopped. This is successfully performed in cases of patients whose trachea is shut up by accident or by inflammation; only it is necessary that this perforation be made into a part of the lungs where it may meet with some of the great pulmonary passages; for if made into some remote part of a lobe, the air cannot find its way into the rest of the lungs through such narrow passages, obstructed too by blood, &c.

We have now explained, on pneumatic principles, the process of inspiration. The expiration is chiefly performed by the natural tone of the parts. In the act of inspiration the ribs were raised and drawn outwards in opposition to the elasticity of the solids themselves; for although the ribs are articulated at their extremities, the articulations are by no means such as to give a free and easy motion like the joints of the limbs. This is particularly the case in the articulations with the sternum, which are by no means fitted for motion. It would seem that the motion really produced here is chiefly by the yielding of the cartilaginous parts and the bending of the rib; when therefore the muscles which produce this effect are allowed to relax, the ribs again collapse. Perhaps this is assisted a little by the action of the long muscles which come down across the ribs without being inserted into them. These may draw them together a little, as we compress a loose bundle by a string. In like manner, when the diaphragm was drawn down, it compressed the abdomen in opposition to the elasticity of all the viscera contained in it, and to the elasticity and tone of integuments and muscles which surround it. When therefore the diaphragm is relaxed, these parts push it up again into its natural situation, and in doing this expel the air from the lungs.

If this be a just account of the matter, expiration should be performed without any effort. This accordingly is the case. We feel that, after having made an ordinary easy inspiration, it requires the continuance of the effort to keep the thorax in this enlarged state, and that all that is necessary for expiration is to cease to act. No person feels any difficulty in emptying the lungs; but weak people often feel a difficulty of inspiration, and compare it to the feeling of a weight on their breast; and expiration is the last motion of the thorax in a dying person. But nature has also given us a mechanism by which we can expire, namely, the abdominal muscles; and when we have finished an ordinary and easy expiration, we can still expel a considerable bulk of air—nearly half the contents of the lungs—by contracting the abdominal muscles. These, by compressing the body, force up its moveable contents against the diaphragm, and cause it to rise further into the thorax, acting in the same manner as when we expel the faeces per anus. When a person breathes out as much air as he can in this manner, he may observe that his ribs do not collapse during the whole operation.

There seems then to be a certain natural unconstrained state of the vesicles of the lungs, and a certain quantity of air necessary for keeping them of this size. It is probable that this state of the lungs gives the freest motion to the blood. Were they more compressed, the blood-vessels would be compressed by the adjoining vesicles; were they more lax, the vessels would be more crooked, and by this means obstructed. The frequent inspirations gradually change this air by mixing fresh air with it, and at every expiration carrying off some of it. In catarrhs and inflammations, especially when attended with suppuration, the small passages into the remote vessels are obstructed, and thus the renewal of air in them will be prevented. The painful feeling which this occasions, causes us to expel the air with violence, shutting the windpipe, till we have exerted strongly with the abdominal muscles, and made a strong compression on the lower part of the thorax. We then open the passage suddenly, and expel the air and obstructing matter by violent coughing.

We have said, that birds exhibit a curious variety in the process of breathing. The muscles of their wings being so very great, required a very extensive insertion, and this is in birds one use of the great breast bone. Another use of it is, to form a firm partition to hinder the action of these muscles from compressing the thorax in the act of flying; therefore the form of their chest does not admit of alternate enlargement and contraction to that degree as in land animals. Moreover, the muscles of their abdomen are also very small; and it would seem that they are not sufficient for producing the compression on the bowels which is necessary for carrying on the process of concoction and digestion. Instead of aiding the lungs, they receive help from them.

In the ostrich, the lungs consist of a fleshy part A, A, (fig. 88) composed of vesicles like those of land animals, and, like theirs, serving to expose the blood to the action of the air. Besides these, they have on each side, four large bags, B, C, D, E, each of which has an orifice G, communicating with the trachea; but the second, C, has an orifice, H, by which it communicates with another bag F, situated below the rest in the abdomen. Now, when the lungs are compressed by the action of the diaphragm, the air in C is partly expelled by the trachea through the orifice G, and partly driven through the orifice H into the bag F, which is then allowed to receive it; because the same action which compresses the lungs enlarges the abdomen. When the thorax is enlarged, the bag C is partly supplied with fresh air through the trachea, and partly from the bag F. As the lungs of other animals resemble a common bellows, the Effects of lungs of birds resemble the smith's bellows with a partition; and anatomists have discovered passages from this part of the lungs into their hollow bones and quills. We do not know all the uses of this contrivance; and only can observe, that this alternate action must assist the muscles of the abdomen in promoting the motion of the food along the alimentary canal, &c. We can distinctly observe in birds that their belly dilates when the chest collapses, and vice versa, contrary to what we see in the land animals. Another use of this double passage may be to produce a circulation of air in the lungs, by which a compensation is made for the smaller surface of action on the blood; for the number of small vesicles, of equal capacity with these large bags, give a much more extensive surface.

If we try to raise mercury in a pipe by the action of the chest alone, we cannot raise it above two or three inches; and the attempt is both painful and hazardous. It is painful chiefly in the breast, and it provokes coughing. Probably the fluids ooze through the pores of the vesicles by the pressure of the surrounding parts. On the other hand, we can by inspiration support mercury about five or six inches high; but this also is very painful, and apt to produce extravasation of blood. This seems to be done entirely by the abdominal muscles.

The operation properly termed sucking, is totally different from breathing, and resembles exceedingly the action of a common pump. Suppose a pipe held in the mouth, and its lower end immersed in water. We fill the mouth with the tongue, bringing it forward, and applying it closely to the teeth and to the palate; we then draw it back, or bend it downwards from the palate behind, thus leaving a void. The pressure of the air on the cheeks immediately depresses them, and applies them close to the gums and teeth; and its pressure on the water in the vessel causes it to rise through the pipe into the empty part of the mouth, which it quickly fills. We then push forward the tip of the tongue, below the water, to the teeth, and apply it to them all round, the water being above the tongue, which is kept much depressed. We then apply the tongue to the palate, beginning at the tip, and gradually going backward in this application. By this means the water is gradually forced backward by an operation similar to that of the gullet in swallowing. This is done by contracting the gullet above, and relaxing it below, just as we would empty a gut of its contents, by drawing our closed hand along it. By this operation the mouth is again completely occupied by the tongue, and we are ready for repeating the operation. Thus the mouth and tongue resemble the barrel and piston of a pump; and the application of the tip of the tongue to the teeth, performs the office of the valve at the bottom of the barrel, preventing the return of the water into the pipe. Although usual, it is not absolutely necessary, to withdraw the tip of the tongue, making a void before the tongue. Sucking may be performed by merely separating the tongue gradually from the palate, beginning at the root. If we withdraw the tip of the tongue a very minute quantity, the water flows back above the tongue.

The action of the tongue in this operation is very powerful; some persons can raise mercury 25 inches; but this strong exertion is very fatiguing, and the soft parts are prodigiously swelled by it. It causes the blood to ooze plentifully through the pores of the tongue, fauces, and palate, in the same manner as if a cupping-glass and syringe were applied to them; and, when the inside of the mouth is excoriated or tender, as is frequent with infants, even a very moderate exertion of this kind is accompanied with extravasation of blood. When children suck the nurse's breast, the milk follows their exertion by the pressure of the air on the breast; and a weak child, or one that withholds its exertions on account of pain from the above mentioned cause, may be assisted by a gentle pressure of the hand on the breast. The infant pupil of nature, without any knowledge of pneumatics, frequently helps itself by pressing its face to the yielding breast.

In the whole of this operation the breathing is performed through the nostrils; and it is a prodigious distress to an infant when this passage is obstructed by mucus. We beg to be forgiven for observing by the way, that this obstruction may be almost certainly removed for a little while, by rubbing the child's nose with any liquid of quick evaporation, or even with water.

The operation in drinking is not very different from that Of drink in sucking. We have indeed little occasion here to suck, but we must do it a little. Dogs, and some other animals, cannot drink, but only lap the water into their mouths with their tongues, and then swallow it. The gallinaceous birds seem to drink very imperfectly. They seem merely to dip their head into the water, up to the eyes, till their mouth is filled with water, and then holding up the head, it gets into the gullet by its weight, and is then swallowed. The elephant drinks in a very complicated manner. He dips his trunk into the water, and fills it by making a void in his mouth. This he does in the contrary way to man. After having depressed his tongue, he begins the application of it to the palate at the root, and by extending the application forward, he expels the air by the mouth which came into it from the trunk. The process here is not very unlike that of the condensing syringe without a piston valve, in which the external air, corresponding to the air in the trunk, enters by the hole in the side, and is expelled through the hole in the end of the barrel; by this operation the trunk is filled with water; then he lifts his trunk out of the water, and bringing it to his mouth, pours the contents into it, and swallows it. On considering this operation, it appears that, by the same process by which the air of the trunk is taken into the mouth, the water could also be taken in, to be afterwards swallowed; but we do not find, upon inquiry, that this is done by the elephant; we have always observed him to drink in the manner now described. In either way it is a double operation, and cannot be carried on any way but by alternately sucking and swallowing, and while one operation is going on, the other is interrupted; whereas man can do both at the same time. Nature seems to delight in exhibiting to rational observers her inexhaustible variety of resource; for many insects which drink with a trunk, drink without interruption; yet we do not call in question the truth of the aphorism, *Natura maxime simplex et tempera sibi consona*, nor doubt but that, if the whole of her purpose were seen, we should find that her process is the simplest possible; for Nature, or Nature's God, is wise above our wisest thoughts, and simplicity is certainly the choice of wisdom; but, alas! it is generally but a small and the most obvious part of her purpose that we can observe or appreciate. We seldom see this simplicity of nature stated to us, except by some system-maker, who has found a principle which somehow tallies with a considerable variety of phenomena, and then cries out, *Frustra sit per plura quod fieri potest per pauciora*.

There is an operation similar to that of the elephant, which Mode of many find a great difficulty in acquiring; namely, keeping up a continued blast with a blow-pipe. We would desire our chemical reader to attend minutely to the gradual action of his blow-pipe in sucking, and he will find it such as we have described. Let him attend particularly to the way in which the tip of the tongue performs the office of a valve, preventing the turn of the water into the pipe; and the same position of the tongue would hinder air from coming into the mouth. Next let him observe, that in swallowing what water he has now got lodged above his tongue, he continues the tip of the tongue applied to the teeth; now let him shut his mouth, keeping his lips firm together, the tip of the tongue at the Effects of teeth, and the whole tongue forcibly kept at a distance from the palate; bring up the tongue to the palate, and allow the tip to separate a little from the teeth, this will expel the air into the space between the fauces and cheeks, and will blow up the cheeks a little; then, acting with the tip of the tongue as a valve, hinder this air from getting back, and depressing the tongue again, more air from the nostrils will get into the mouth, which may be expelled into the space without the teeth as before, and the cheeks will be more inflated. Continue this operation, and the lips will no longer be able to retain it, and it will ooze through as long as the operation is continued. When this has become familiar and easy, take the blow-pipe, and there will be no difficulty in maintaining a blast as uniform as a smith's bellows, breathing all the while through the nostrils. The only difficulty is the holding the pipe. This fatigues the lips; but it may be removed by giving the pipe a convenient shape, a pretty flat oval, and wrapping it round with leather or thread.

Another phenomenon depending on the principles already established, is the land and sea-breeze in the warm countries. We have seen that air expands exceedingly by heat; therefore heated air, being lighter than an equal bulk of cold air, must rise in it. If we lay a hot stone in the sunshine in a room, we shall observe the shadow of the stone surrounded with a fluttering shadow of different degrees of brightness, and that this flutter rises rapidly in a column above the stone. If we hold an extinguished candle near the stone, we shall see the smoke move towards the stone, and then ascend from it. Now, suppose an island receiving the first rays of the sun in a perfectly calm morning; the ground will soon be warmed, and will warm the contiguous air. If the island be mountainous, this effect will be more remarkable; because the inclined sides of the hills will receive the light more directly. The midland air will therefore be most warmed. The heated air will rise, and that in the middle will rise fastest; and thus a current of air upwards will begin, which must be supplied by air coming in from all sides, to be heated and to rise in its turn; so that the morning sea-breeze is produced, and continues all day. This current will frequently be reversed during the night, by the air cooling and gliding down the sides of the hills, and we shall have the land-breeze.

It is owing to the same cause that we have a circulation of air in mines which have the mouths of their shafts of unequal heights. The temperature under ground is pretty constant through the whole year, while that of the atmosphere is extremely variable. Now, suppose a mine having a long horizontal drift, communicating between two pits or shafts, and that one of these shafts terminates in a valley, while the other opens on the brow of a hill perhaps 100 feet higher. Let us further suppose it summer, and the air heated to $65^\circ$, while the temperature of the earth is but $45^\circ$; this last will be also the temperature of the air in the shafts and the drift. Now, since air expands nearly $\frac{24}{10,000}$ parts in 10,000 by one degree of heat, we shall have an odds of pressure at the bottom of the two shafts equal to nearly the 20th part of the weight of a column of air 100 feet high (100 feet being supposed the difference of the heights of the shafts.) This will be about six ounces on every square foot of the section of the shaft. If this pressure could be continued, it would produce a prodigious current of air down the long shafts, the drift, and up the short shaft. The weight of air acting through 100 feet would communicate to it the velocity of 80 feet per second: divide this by $\sqrt{20}$, that is, by $4\sqrt{5}$, and we shall have 18 feet per second for the velocity: this is the velocity of what is called a brisk gale. This pressure would be continued, if the warm air which enters the long shaft were cooled and condensed as fast as it comes in; but this is not the case. It is however cooled and condensed, and a current is produced sufficient to make an abundant circulation of air along the whole passage; and care is taken to dispose the shafts and conduct the passages in such a manner that no part of the mine is out of the circle. When any new lateral drift is made, the renewal of air at its extremity becomes more imperfect as it advances; and when it is carried a certain length, the air stagnates and becomes suffocating, till either a communication can be made with the rest of the mine, or a shaft be made at the end of this drift.

As this current depends entirely on the difference of temperature between the air below and that above, it must cease when this difference ceases. Accordingly, in the spring and autumn, the miners complain much of stagnation; but in summer they never want a current from the deep pits to the shallow, nor in the winter a current from the shallow pits to the deep ones. It frequently happens also, that in mineral countries the chemical changes which are going on in different parts of the earth occasion differences of temperature sufficient to produce a sensible current.

And this naturally leads us to consider a very important effect of the expansion and consequent ascent of air by heat, namely, the drawing, as it is called, of chimneys. The air which has contributed to the burning of fuel must be intensely heated, and will rise in the atmosphere. This will also be the case with much of the surrounding air which has come very near the fire, although not in contact with it. If this heated air be made to rise in a pipe, it will be kept together, and therefore will not soon cool and collapse: thus we shall obtain a long column of light air, which will rise with a force so much the greater as the column is longer or more heated. Therefore the taller we make the chimney, or the hotter we make the fire, the more rapid will be the current, or the draught or suction, as it is injudiciously called, will be so much the greater. The ascensional force is the difference between the weight of the column of heated air in the funnel and a column of the surrounding atmosphere of equal height. We increase the draught, therefore, by increasing the perpendicular height of the chimney. Its length in a horizontal direction gives no increase, but, on the contrary, diminishes the draught by cooling the air before it gets into the effective part of the funnel. We increase the draught also by obliging all the air which enters the chimney to come very near the fuel; therefore a low mantle-piece will produce this effect; also filling up all the spaces on each side of the grate. When much air gets above the fire, by having a lofty mantle-piece, the general mass of air in the chimney cannot be much heated. Hence it must happen that the greatest draught will be produced by bringing down the mantle-piece to the very fuel; but this converts a fire-place into a furnace, and by thus sending the whole air through the fuel, causes it to burn with great rapidity, producing a prodigious heat; and this producing an increase of ascensional force, the current becomes furiously rapid, and the heat and consumption of fuel immense. If the fire-place be a cube of a foot and a half, and the front closed by a door, so that all the air must enter through the bottom of the grate, a chimney of fifteen or twenty feet high, and sufficiently wide to give passage to all the expanded air which can pass through the fire, will produce a current which will roar like thunder, and a heat sufficient to run the whole inside into a lump of glass.

All that is necessary, however, in a chamber fire-place, is a current sufficiently great for carrying up the smoke and vitiated air of the fuel. And as we want also the enlivening light and flutter of the fire, we give the chimney-piece both a much greater height and width than what is merely necessary for carrying up the smoke, only wishing to have the current sufficiently determinate and steady for counteracting any occasional tendency which it may sometimes have to come into the room. By allowing a greater quantity of air to get into the chimney, heated only to a mode- Effects of rate degree, we produce a more rapid renewal of the air of the room; did we oblige it to come so much nearer the fire as to produce the same renewal of the air in consequence of a more rapid current, we should produce an inconvenient heat. But in this country, where pit-coal is in general so very cheap, we carry this indulgence to an extreme; or rather we have not studied how to get all the desired advantages with economy. A much smaller renewal of air than we commonly produce is abundantly wholesome and pleasant, and we may have all the pleasure of the light and flame of the fuel at much less expense, by contracting greatly the passage into the vent. The best way of doing this is by contracting the brick-work on each side behind the mantelpiece, and reducing it to a narrow parallelogram, having the back of the vent for one of its long sides. Make an iron plate to fit this hole, of the same length, but broader, so that it may lie sloping, its lower edge being in contact with the foreside of the hole, and its upper edge leaning on the back of the vent. In this position it shuts the hole entirely. Now let the plate have a hinge along the front or lower edge, and fold up like the lid of a chest. We shall thus be able to enlarge the passage at pleasure. In a fire-place fit for a room of 24 feet by 18, if this plate be about 18 inches long from side to side, and folded back within an inch or an inch and a half of the wall, it will allow passage for as much air as will keep up a very cheerful fire; and by raising or lowering this register, the fire may be made to burn more or less rapidly. A free passage of half an inch will be sufficient in weather that is not immoderately cold. The principle on which this construction produces its effect is, that the air which is in the front of the fire, and much warmed by it, is not allowed to get into the chimney, where it would be immediately hurried up the vent, but rises up to the ceiling and is diffused over the whole room. This double motion of the air may be distinctly observed by opening a little of the door and holding a candle in the way. If the candle be held near the floor, the flame will be blown into the room; but if held near the top of the door, the flame will be blown outward.

But the most perfect method of warming an apartment in the temperate climates, where we can indulge in the cheerfulness and sweet air produced by an open fire, is what we call a stove-grate, and our neighbours on the Continent call a chapelle, from its resemblance to the chapels or oratories in the great churches.

In the great chimney-piece, which, in this case, may be made even larger than ordinary, is set a smaller one fitted up in the same style of ornament, but of a size no greater than is sufficient for holding the fuel. The sides and back of it are made of iron (cast iron is preferable to hammered iron, because it does not so readily calcine), and are kept at a small distance from the sides and back of the main chimney-piece, and are continued down to the hearth, so that the ash-pit is also separated. The pipe or chimney of the stove grate is carried up behind the ornaments of the mantle-piece till it rises above the mantle-piece of the main chimney-piece, and is fitted with a register or damper-plate turning round a traverse axis. The best form of this register is that which we have recommended for an ordinary fire-place, having its axis or joint close at the front; so that when it is open or turned up, the burnt air and smoke striking it obliquely, are directed with certainty into the vent, without any risk of reverberating and coming out into the room. All the rest of the vent is shut up by iron-plates or brick-work out of sight.

The effect of this construction is very obvious. The fuel, being in immediate contact with the back and sides of the grate, heats them to a great degree, and they heat the air contiguous to them. This heated air cannot get up the vent, because the passages above these spaces are shut up. It therefore comes out into the room; some of it goes into the real fire-place and is carried up the vent, and the rest rises to the ceiling and is diffused over the room.

It is surprising to a person who does not consider it with skill, how powerfully this grate warms a room. Less than one-fourth of the fuel consumed in an ordinary fire-place is sufficient; and this with the same cheerful blazing hearth and salutary renewal of air. It even requires attention to keep the room cool enough. The heat communicated to those parts in contact with the fuel is needlessly great; and it will be a considerable improvement to line this part with very thick plates of cast-iron, or with tiles made of fire-clay which will not crack with the heat. These, being very bad conductors, will make the heat, ultimately communicated to the air, very moderate. If, with all these precautions, the heat should be found too great, it may be brought under perfect management by opening passages into the vent from the lateral spaces. These may be valves or trap-doors moved by rods concealed behind the ornaments.

Thus we have a fire-place under the most complete regulation, where we can always have a cheerful fire without being for a quarter of an hour inconvenienced by the heat; and we can as quickly raise our fire, when too low, by hanging on a plate of iron on the front, which shall reach as low as the grate. This in five minutes will blow up the fire into a glow; and the plate may be sent out of the room, or set behind the stove-grate out of sight.

The propriety of inclosing the ash-pit is not so obvious; but if this be not done, the light ashes, not finding a ready passage up the chimney, will come out into the room along with the heated air.

Under this head we shall next give a general account of description of the method of warming apartments by warming stoves. A stove in general is a fire-place shut up on all apartments sides, having only a passage for admitting the air to support by stoves the fire, and a tube for carrying off the vitiated air and smoke; and the air of the room is warmed by coming into contact with the outside of the stove and flue. The general principle of construction, therefore, is very simple. The air must be made to come into as close contact as possible with the fire, or even to pass through it, and this in such quantities as just to consume a quantity of fuel sufficient for producing the heat required; and the stove must be so constructed, that both the burning fuel and the air which has been heated by it shall be applied to as extensive a surface as possible of furnace, all in contact with the air of the room; and the heated air within the stove must not be allowed to get into the funnel which is to carry it off till it is too much cooled to produce any considerable heat on the outside of the stove.

In this temperate climate no great ingenuity is necessary for warming an ordinary apartment; and stoves are made rather to please the eye as furniture than as economical substitutes for an open fire of equal calorific power. But our neighbours on the Continent, and especially towards the north, where the cold of winter is intense and fuel very dear, have bestowed much attention on their construction, and have combined ingenious economy with every elegance of form. Nothing can be handsomer than the stoves of Fayencerie that are to be seen in French Flanders, or the Russian stoves at St. Petersburg, finished in stucco. Our readers will not, therefore, be displeased with a description of them. In this place, however, we shall only consider a stove in general as a subject of pneumatical discussion, and refer our readers to the article STOVE for stoves as articles of domestic accommodation.

The general form, therefore, of a stove, and of which all others are only modifications adapted to circumstantial form of a cles of utility or taste, is as follows:—MIKL (fig. 79.) is stove. a quadrangular box of any size in the directions MILK. The inside width from front to back is pretty constant, never less than 10 inches, and rarely extending to 20;

The included space is divided by a great many partitions. The lowest chamber B is the receptacle for the fuel, which lies on the bottom of the stove without any grate; this fireplace has a door AO turning on hinges, and in this door is a very small wicket P; the roof of the fireplace extends to within a very few inches of the farther end, leaving a narrow passage B for the flame. The next partition c C is about eight inches higher, and reaches almost to the other end, leaving a narrow passage for the flame at C. The partitions are repeated above, at the distance of eight inches, leaving passages at the ends, alternately disposed as in the figure; the last of them H communicates with the room vent. This communication may be regulated by a plate of iron, which can be slid across it by means of a rod or handle which comes through the side. The more usual way of shutting up this passage is by a sort of pan or bowl of earthen ware, which is inverted over it with its brim resting in sand contained in a groove formed all round the hole. This damper is introduced by a door in the front, which is then shut. The whole is set on low pillars, so that its bottom may be a few inches from the floor of the room. It is usually placed in a corner, and the apartments are so disposed that their chimneys can be joined in stacks as with us.

Some straw or wood shavings are first burnt on the hearth at its farther end. This warms the air in the stove, and creates a determined current. The fuel is then laid on the hearth close by the door, and pretty much piled up. It is now kindled; and the current being already directed to the vent, there is no danger of any smoke coming out into the room. Effectually to prevent this, the door is shut, and the wicket P opened. The air supplied by this, being directed to the middle or bottom of the fuel, quickly kindles it, and the operation goes on.

The aim of this construction is very obvious. The flame and heated air are retained as long as possible within the body of the stove by means of the long passages; and the narrowness of these passages obliges the flame to come in contact with every particle of soot, so as to consume it completely, and thus convert the whole combustible matter of the fuel into heat. For want of this, a very considerable portion of our fuel is wasted by our open fires, even under the very best management. The soot which sticks to our vents is very inflammable, and a pound weight of it will give as much if not more heat than a pound of coal. And what sticks to our vents is very inconsiderable in comparison with what escapes unconsumed at the chimney top. In fires of green wood, peat, and some kinds of pit-coal, nearly one-fifth of the fuel is lost in this way; but in these stoves there is hardly ever any mark of soot to be seen; and even this small quantity is produced only after lighting the fires. The volatile inflammable matters are expelled from parts much heated indeed, but not so hot as to burn; and some of it charred or half-burnt cannot be any further consumed, being enveloped in flame and air already vitiated and unfit for combustion. But when the stove is well heated, and the current brisk, no part of the soot escapes the action of the air.

The hot air retained in this manner in the body of the stove is applied to its sides in a very extended surface. To increase this still more, the stove is made narrower from front to back in its upper part; a certain breadth is necessary below, that there may be room for fuel. If this breadth were preserved all the way up, much heat would be lost, because the heat communicated to the partitions of the stove does no good. By diminishing their breadth, the proportion of useful surface is increased. The whole body of the stove may be considered as a long pipe folded up, and its effect would be the greatest possible if it really were so; that is, if each partition eC, dD, &c., were split into two, and a free passage allowed between them for the air of the room. Something like this will be observed afterwards in some German stoves.

It is with the same view of making an extensive application of a hot surface to the air, that the stove is not built in the wall, not even in contact with it, nor with the floor; for by its detached situation, the air in contact with the back, and with the bottom, where it is hottest, is warmed, and contributes at least one-half of the whole effect; for the great heat of the bottom makes its effect on the air of the room at least equal to that of the two ends. Sometimes a stove makes part of the wall between two small rooms, and is found sufficient.

It must be remarked, on the whole, that the effect of a stove depends much on keeping in the room the air already heated by it. This is so remarkably the case, that a small open fire in the same room will be so far from increasing its heat, that it will greatly diminish it; it will even draw the warm air from a suite of adjoining apartments. This is distinctly observed in the houses of the English merchants in St. Petersburg; their habits of life in Britain make them uneasy without an open fire in their sitting rooms; and this obliges them to heat all their stoves twice a-day, and their houses are cooler than those of the Russians, who heat them only once. In many German houses, especially of the lower class, the fireplace of the stove does not open into the room, but into the yard or a lobby, where all the fires are lighted and tended; by this means is avoided the expense of warm air which must have been carried off by the stove; but it is evident, that this must be very unpleasant, and cannot be wholesome. We must breathe the same quantity of stagnant air loaded with all the vapours and exhalations which must be produced in every inhabited place. Going into one of these houses from the open air, is like putting one's head into a stew-pan or under a pie-crust, and quickly nauseates us who are accustomed to fresh air and cleanliness. In these countries it is a matter almost of necessity, to fumigate the rooms with frankincense and other gums burnt. The censer in ancient worship was in all probability an utensil introduced by necessity for sweetening or rendering tolerable the air of a crowded place; and it is a constant practice in the Russian houses for a servant to go round the room after dinner, waving a censer with some gums burning on bits of charcoal.

The account now given of stoves for heating rooms, and of hot walls in construction, will equally apply to hot walls in gardening, whether within or without doors. The only new circumstance which this employment of a flue introduces, is the attention which must be paid to the equality of the heat, and the gradation which must be observed in different parts of the building. The heat in the flue gradually diminishes as it recedes from the fireplace, because it is continually giving out heat to the flue. It must therefore be so conducted through the building by frequent returns, that in every part there may be a mixture of warmer and cooler branches of the flue, and the final chimney should be close by the fireplace. It would, however, be improper to run the flue from the end of the floor up to the ceiling, where the second horizontal pipe would be placed, and then return it downward again and make the third horizontal flue adjoining to the first, &c. This would make the middle of the wall the coldest. If it is the flue of a greenhouse, this would be highly improper, because the upper part of the wall can be very little employed; and in this case it is bet-

Effects of the pressure of the air.

Malt-kilns are a species of stove which merit our attention. Many attempts have been made to improve them on the principle of flue stoves; but they have been unsuccessful, because heat is not what is chiefly wanted in malting; it is a copious current of very dry air to carry off the moisture.

All that is to be attended to in the different kinds of melting furnaces is, that the current of air be sufficiently rapid, and that it be applied in as extensive a surface as possible to the substance to be melted. The more rapid the current it is the hotter, because it is consuming more fuel; and therefore its effect increases in a higher proportion than its rapidity. It is doubly effectual if twice as hot; and if it then be twice as rapid, there is twice the quantity of doubly hot air applied to the subject; it would therefore be four times more powerful. This is procured by raising the chimney of the furnace to a greater height. The close application of it to the subject can hardly be laid down in general terms, because it depends on the precise circumstances of each case.

Current in reverberatory furnaces.

In reverberatory furnaces, such as refining furnaces for gold, silver, and copper, the flame is made to play over the surface of the melted metal. This is produced entirely by the form of the furnace, by making the arch of the furnace as low as the circumstances of the manipulation will allow. See Furnace. Experience has pointed out in general the chief circumstances of their construction, viz., that the fuel should be at one end on a grate, through which the air enters to maintain the fire; and that the metal should be placed on a level floor between the fire and the tall chimney which produces the current. But there is no kind of furnace more variable in its effect, and almost every place has a small peculiarity of construction, on which its pre-eminence is rested. This has occasioned many whimsical varieties in their form. This uncertainty seems to depend much on a circumstance rather foreign to our present purpose; but as we do not observe it taken notice of by mineralogical writers, we beg leave to mention it here. It is not heat alone that is wanted in the refining of silver by lead, for instance. We must make a continual application to its surface of air, which has not contributed to the combustion of the fuel. Any quantity of the hottest air, already saturated with the fuel, may play on the surface of the metal for ever, and keep it in the state of most perfect fusion, but without refining it in the least. Now, in the ordinary construction of a furnace, this is much the case. If the whole air has come in by the grate, and passed through the middle of the fuel, it can hardly be otherwise than nearly saturated with it; and if air be also admitted by the door, which is generally done or something equivalent, the pure air lies above the vitiated air, and during the passage along the horizontal part of the furnace, and along the surface of the metal, it still keeps above it, at least there is nothing to promote their mixture. Thus the metal does not come into contact with air fit to act on the base metal and calcine it, and the operation of refining goes on slowly. Trifling circumstances in the form of the arch or canal may tend to promote the jumbling of the airs together, and thus render the operation more expeditions; and as these are but ill understood, or perhaps this circumstance not attended to, no wonder that we see these considered as so many nostrums of great importance. It were therefore worth while to try the effect of changes in the form of the roof directed to this very circumstance. Perhaps some little prominence down from the arch of the reverberatory would have this effect, by suddenly throwing the current into confusion. If the additional length of passage do not cool the air too much, we should think that if there were interposed between the fuel and the refining floor a passage twisted like a cork-screw, making just half a turn, it would be most effectual; for we imagine, that the two airs, keeping each to their respective sides of the passage, would by this means be turned upside down, and that the pure stratum would now be in contact with the metal, and the vitiated air would be above it.

The glass-house furnace exhibits the chief variety in the management of the current of heated air. In this it is necessary that the hole at which the workman dips his pipe house furnaces into the pot shall be as hot as any part of the furnace. This could never be the case, if the furnace had a chimney situated in a part above the dipping-hole; for in this case cold air would immediately rush in at the hole, play over the surface of the pot, and go up the chimney. To prevent this the hole itself is made the chimney; but as this would be too short, and would produce very little current and very little heat, the whole surface is set under a tall dome. Thus the heated air from the real furnace is confined in this dome, and constitutes a high column of very light air, which will therefore rise with great force up the dome, and escape at the top. The dome is therefore the chimney, and will produce a draught or current proportioned to its height. Some are raised above a hundred feet. When all the doors of this house are shut, and thus no supply given except through the fire, the current and heat become prodigious. This, however, cannot be done, because the workmen are in this chimney, and must have respirable air. But notwithstanding this supply by the house-doors, the draught of the real furnace is vastly increased by the dome, and a heat produced sufficient for the work, and which could not have been produced without the dome.

This has been applied with great ingenuity and effect to Cotterel's furnace for melting iron from the ore, and an iron finery, improved both without a blast. The common blast iron furnace is well known. It is a tall cone with the apex undermined, iron from the ore and fluxes are thrown into this cone mixed intimately with the fuel till it is full, and the blast of most powerful bellows is directed into the bottom of this cone through a hole in the side. The air is thrown in with such force, that it makes its way through the mass of matter, kindles the fuel in its passage, and fluxes the materials, which then drop down into a receptacle below the blast-hole, and thus the passage for the air is kept unobstructed. It was thought impossible to produce or maintain this current without bellows; but Mr. Cotterel, an ingenious founder, tried the effect of a tall dome placed over the mouth of the furnace, and though it was not half the height of many glass-house domes it had the desired effect.

The last application which we shall make of the currents produced by heating the air is to the freeing mines, ships, air applied prisons, &c. from the damp and noxious vapours which frequently infest them. As a drift or work is carried on in the mines, &c., mine, let a trunk of deal boards, about six or eight inches square, be laid along the bottom of the drift, communicating with a trunk carried up in the corner of one of the shafts. Let the top of this last trunk open into the ash-pit of a small furnace, having a tall chimney. Let fire be kindled in the furnace; and when it is well heated, shut the fire-place and ash-pit doors. There being no other supply for the current produced in the chimney of this furnace, the air will flow into it from the trunk, and will bring along with it all the offensive vapours. This is the most effectual method yet found out. In the same manner may trunks be conducted into the ash-pit of a furnace from the cells of a prison or the wards of an hospital.

In the account which we have been giving of the manage- ment of air in furnaces and common fires, we have frequently mentioned the immediate application of air to the burning fuel as necessary for its combustion. This is a general fact.

In order that any inflammable body may be readily inflamed, and its combustible matter consumed and ashes produced, it is not enough that the body be made hot. A piece of charcoal inclosed in a box of iron may be kept red hot for ever, without wasting its substance in the smallest degree.

It is further necessary that it be in contact with a particular species of air, which constitutes nearly one-fourth of the air of the atmosphere, viz. the vital air or oxygen of Lavoisier. It was called empyreal air by Scheele, who first observed its indispensable use in maintaining fire; and it appears, that, in contributing to the combustion of an inflammable body, this air combines with some of its ingredients, and becomes fixed air, suffering the same change as by the breathing of animals. Combustion may therefore be considered as a union of the inflammable body with oxygen.

This doctrine was first promulgated by the celebrated Dr. Hooke in his Micrographia, published in 1660, and afterwards improved in his Treatise on Lamps. It is now completely established, and considered as a new discovery. It is for this reason, that in fire-places of all kinds we have directed the construction, so as to produce a close application of the air to the fuel. It is quite needless at this day to enter into the discussions which formerly occupied philosophers about the manner in which the pressure and elasticity of the air promoted combustion. Many experiments were made in the seventeenth century by the first members of the Royal Society, to discover the office of air in combustion. It was thought that the flame was extinguished in rare air for want of a pressure to keep it together; but this did not explain its extinction when the air was not renewed. These experiments were long retained in courses of experimental philosophy, as they were judiciously styled; but they neither gave information, nor tended to the illustration of any pneumatical doctrine: they are of course omitted in this place. In short, it is now fully established, that it is not a mechanical but a chemical phenomenon. We can only inform the chemist, that a candle will consume faster in the low countries than in the elevated regions of Quito and Gondar, because the air is nearly one half denser below, and will act proportionally faster in decomposing the candle.

We shall conclude this part of our subject with the explanation of a curious phenomenon observed in many places. Certain springs or fountains are observed to have periods of repletion and scantiness, or seem to ebb and flow at regular intervals; and some of these periods are of a complicated nature. Thus a well will have several returns of high and low water, the difference of which gradually increases to a maximum, and then diminishes, just as we observe in the ocean. A very ingenious and probable explanation of this has been given in No. 424 of the Philosophical Transactions, by Mr. Atwell.

Let ABCD (fig. 90.) represent a cavern, into which water is brought by the subterraneous passage OT. Let

Fig. 90.

it have an outlet MNP, of a crooked form, with its highest part N considerably raised above the bottom of the cavern, and thence sloping downwards into lower ground, and terminating in an open well at P. Let the dimensions of this canal be such that it will discharge much more water than is supplied by TO. All this is very natural, and may be very common. The effect of this arrangement will be a remitting spring at P; for when the cavern is filled higher than the point N, the canal MNP will act as a syphon; and, by the conditions assumed, it will discharge the water faster than TO supplies it; it will therefore run it dry, and then the spring at P will cease to furnish water. After some time the cavern will again be filled up to the height N, and the flow at P will recommence.

If, besides this supply, the well P also receive water from a constant force, we shall have a reciprocating spring. The situation and dimensions of this syphon canal, and the supply of the feeder, may be such, that the efflux at P will be constant. If the supply increase in a certain degree, a reciprocation will be produced at P with very short intervals; if the supply diminishes considerably, we shall have another kind of reciprocation with great intervals and great differences of water.

If the cavern have another simple outlet R, new varieties will be produced in the spring P, and R will afford a copious spring. Let the mouth of R, by which the water enters into it from the cavern, be lower than N, and let the supply of the feeding spring be no greater than R can discharge, we shall have a constant spring from R, and P will give no water. But suppose that the main feeder increases in winter or in rainy seasons, but not so much as will supply both P and R, the cavern will fill till the water gets over N, and R will be running all the while; but soon after P has begun to flow, and the water in the cavern sinks below R, the stream from R will stop. The cavern will be emptied by the syphon canal MNP, and then P will stop. The cavern will then begin to fill, and when near full P will give a little water, and soon after P will run and R stop as before, &c. Desaguliers shows (vol. ii. p. 177, &c.) in what manner a prodigious variety of periodical ebbs and flows may be produced by underground canals, which are extremely simple and probable.

We shall conclude this article with the descriptions of Account of some pneumatical machines or engines which have not been particularly noticed under their names in the former volumes of this work.

Bellows are of most extensive and important use; and it will be of service to describe such as are of uncommon construction and power, sufficient for the great operations in metallurgy.

It is not the impulsive force of the blast that is wanted in most cases, but merely the copious supply of air, to produce the rapid combustion of inflammable matter; and the service would be better performed in general if this could be done with moderate velocities, and an extended surface. What are called air-furnaces, where a considerable surface of inflammable matter is acted on at once by the current which the mere heat of the expended air has produced, are found more operative in proportion to the air expended than blast furnaces animated by bellows; and we doubt not but that the method proposed by Mr. Cotterel, which we have already mentioned, of increasing this current in a melting furnace by means of a dome, will in time supersede the blast furnaces. There is indeed a great impulsive force required in some cases; as for blowing off the scorie from the surface of silver or copper in refining furnaces, or for keeping a clear passage for the air in the great iron furnace.

In general, however, we cannot procure this abundant supply of air any other way than by giving it a great velocity by means of a great pressure, so that the general construction of bellows is pretty much the same in all kinds. The air is admitted into a very large cavity, and then expelled from it through a small hole.

The furnaces at the mines having been greatly enlarged, it was necessary to enlarge the bellows also; and the northern bellows becoming exceedingly expensive, wooden ones were substituted in Germany about the beginning of the seventeenth century, and from them became general throughout Europe. They consist of a wooden box ABCPFE, fig. 91.

Fig. 91.

which has its top and two sides flat or straight, and the end BAE formed into an arched or cylindrical surface, of which the line FP at the other end is the axis. This box is open below, and receives within it the shallow box KHGNML, fig. 92, which exactly fills it. The line FP

Fig. 92.

of the one coincides with FM of the other, and along this line is a set of hinges on which the upper box turns as it rises and sinks. The lower box is made fast to a frame fixed in the ground. A pipe OQ proceeds from the end of it, and terminates at the furnace, where it ends in a small pipe called the teucer or tugere. This lower box is open above, and has in its bottom two large valves V, V, fig. 93, opening inwards. The conducting pipe is sometimes furnished with a valve opening outwards, to prevent burning coals from being sucked into the bellows when the upper box is drawn up. The joint along PF is made tight by thin leather nailed along it. The sides and ends of the fixed box are made to fit the sides and curved end of the upper box, so that this last can be raised and lowered round the point FP without sensible friction, and yet without suffering much air to escape; but as this would not be sufficiently air-tight by reason of the shrinking and warping of the wood, a farther contrivance is adopted. A slender lath of wood, divided into several joints, and covered on the outer edge with very soft leather, is laid along the upper edges of the sides and ends of the lower box. This lath is so broad, that when its inner edge is even with the inside of the box, its outer edge projects about an inch. It is kept in this position by a number of steel wires, which are driven into the bottom of the box, and stand up touching the sides, as represented in fig. 94, where a b c are the wires, and e the lath, projecting over the outside of the box. By this contrivance the laths are pressed close to the sides and curved end of the moveable box, and the spring wires yield to all their inequalities. A bar of wood RS, fig. 91, is fixed to the upper board, by which it is either raised by machinery, to sink again by its own weight, having an additional load laid on it, or it is forced downward by a crank or wiper of the machinery, and afterwards raised.

The operation here is precisely similar to that of blowing with a chamber-bellows. When the board is lifted up, the air enters by the valves V, V, fig. 93, and is expelled at the pipe OQ by depressing the boards. There is therefore no occasion to insist on this point.

These bellows are made of a very great size, AD being 16 feet, AB five feet, and the circular end AE also five feet. The rise, however, is but about 3 or 3½ feet. They expel at each stroke about 50 cubic feet of air, and they make about 8 strokes per minute.

Such are the bellows in general use on the continent. We have adopted a different form in this kingdom, which seems much preferable. We use an iron or wooden cylinder, with a piston sliding along it. This may be made with much greater accuracy than the wooden boxes, at less expense, if of wood, because it may be of cooper's work, held together by hoops; but the great advantage of this form is its being more easily made air-tight. The piston is surrounded with a broad strap of thick and soft leather, and it has around its edge a deep groove, in which is lodged a quantity of wool. This is called the packing or stuffing, and keeps the leather very closely applied to the inner surface of the cylinder. Iron cylinders may be very neatly bored and smoothed, so that the piston, even when very tight, will slide along it very smoothly. To promote this, a quantity of black lead is ground very fine with water, and a little of this is smeared on the inside of the cylinder from time to time.

The cylinder has a large valve, or sometimes two, in the bottom, by which the atmospheric air enters when the piston is drawn up. When the piston is thrust down, this air is expelled along a pipe of great diameter, which terminates in the furnace with a small orifice.

This is the simplest form of bellows which can be conceived. It differs in nothing but size from the bellows used by the rudest nations. The Chinese smiths have a bellows very similar, being a square pipe of wood ABCDE, fig. 95, with a square board G which exactly fits it, moved by the handle FG. At the farther end is the blast pipe CK, and on each side of it a valve in the end of the square pipe, opening inwards. The piston is sufficiently tight for their purposes without any leathering.

The piston of this cylinder bellows is moved by machinery. In some blast engines the piston is simply raised by the machine, and then let go, and it descends by its own weight, and compresses the air below it to such a degree, that the velocity of efflux becomes constant, and the piston descends uniformly; for this purpose it must be loaded with a proper weight. This produces a very uniform blast, except at the very beginning, whilst the piston falls suddenly and compresses the air; but in most engines the piston rod is forced down the cylinder with a determined motion, by means of a beam, crank, or other contrivance. This Pneumatic gives a more unequal blast, because the motion of the piston is necessarily slow in the beginning and end of the stroke, and quicker in the middle.

But in all it is plain that the blast must be desultory. It ceases while the piston is rising; for this reason it is usual to have two cylinders, as it was formerly usual to have two bellows which worked alternately. Sometimes three or four are used, as at the Carron iron-works. This makes a blast abundantly uniform.

But an uniform blast may be made with a single cylinder, by making it deliver its air into another cylinder, which has a piston exactly fitted to its bore, and loaded with a sufficient weight. The blowing cylinder ABCD, fig. 96, has its piston P worked by a rod NP, connected by double chains with the arched head of the working beam NO, moving round a gudgeon at R. The other end O of this beam is connected by the rod OP, with the crank PQ of a wheel machine; or it may be connected with a piston of a steam-engine, &c., &c. The blowing cylinder has a valve or valves E in its bottom, opening inwards. There proceeds from it a large pipe CF, which enters the regulating cylinder GHKL, and has a valve at top to prevent the air from getting back into the blowing cylinder. It is evident that the air forced into this cylinder must raise its piston L, and that it must afterwards descend, while the other piston is rising. It must descend uniformly, and make a perfectly equable blast.

Observe, that if the piston L be at the bottom when the machine begins to work, it will be at the bottom at the end of every stroke if the tuyere T emits as much air as the cylinder ABCD furnishes; nay, it will lie a while at the bottom, for, while it was rising, air was issuing through T. This would make an interrupted blast. To prevent this, the orifice T must be lessened; but then there will be a surplus of air at the end of each stroke, and the piston L will rise continually, and at last get to the top, and allow air to escape. It is just possible to adjust circumstances, so that neither shall happen. This is done easier by putting a stop in the way of the piston, and putting a valve on the piston, or on the conducting pipe KST, loaded with a weight a little superior to the intended elasticity of the air in the cylinder. Therefore, when the piston is prevented by the stop from rising, the snifting valve, as it is called, is forced open, the superfluous air escapes, and the blast preserves its uniformity.

It may be of use to give the dimensions of a machine of this kind, which worked for many years at a very great furnace, and given satisfaction.

The diameter of the blowing cylinder is 5 feet, and the length of the stroke is 4½. Its piston is loaded with 3½ tons. It is worked by a steam-engine whose cylinder is 3 feet 4 inches wide, with a six-feet stroke. The regulating cylinder is 8 feet wide, and its piston is loaded with 8½ tons, making about 2,653 pounds on the square inch; and it is very nearly in equilibrium with the load on the piston of the blowing cylinder. The conducting pipe KST is 12 inches in diameter, and the orifice of the tuyere was 8½ inches in diameter when the engine was erected, but it has gradually enlarged by reason of the intense heat to which it is exposed. The snifting valve is loaded with 3 pounds on the square inch.

When the engine worked briskly, it made 18 strokes per minute, and there was always much air discharged by the snifting valve. When the engine made 15 strokes per minute, the snifting valve opened but seldom, so that things were nearly adjusted to this supply. Each stroke of the blowing cylinder sent in 118 cubic feet of common air. The ordinary pressure of the air being supposed 143 pounds on an inch, the density of the air in the regulating cylinder must be \(\frac{1475 + 263}{1475} = 1.1783\), the natural density being 1.

This machine gives an opportunity of comparing the expense of air with the theory. It must, at the rate of 15 strokes, expel 30 cubic feet of air in a second through a hole of 1½ inches in diameter. This gives a velocity of near 2000 feet per second, and of more than 1600 feet for the condensed air. This is vastly greater than the theory can give, or is indeed possible; for air does not rush into a void with so great velocity. It shows with great evidence, that a vast quantity of air must escape round the two pistons. Their united circumferences amount to above 40 feet, and they move in a dry cylinder. It is impossible to prevent a very great loss. Accordingly, a candle held near the edge of the piston L has its flame very much disturbed. This case, therefore, gives no hold for a calculation; and it suggests the propriety of attempting to diminish this great waste.

This has been very ingeniously done, in part at least, at some other furnaces. At a certain foundry, near Glasgow, the blowing cylinder, also worked by a steam-engine, delivers its air into a chest without a bottom, which is immersed in a large cistern of water, and supported at a small height from the bottom of the cistern, and has a pipe from its top leading to the tuyere. The water stands about five feet above the lower brim of the regulating air-chest, and by its pressure gives the most perfect uniformity of blast, without allowing a particle of air to get off by any other passage besides the tuyere. This is a very effectual regulator, and must produce a great saving of power, because a smaller blowing cylinder will thus supply the blast. We must observe, that the loss round the piston of the blowing cylinder remains undiminished.

A blowing machine was erected many years ago at Châtillon in France on a principle considerably different, and which must be perfectly air-tight throughout. Two cylinders A, B, (fig. 97) loaded with great weights, were suspended at the ends of the lever CD, moving round the gudgeon E. From the top F, G of each there was a large flexible pipe which united in H, from whence a pipe KT led to the tuyere T. There were valves at F and G opening outwards, or into the flexible pipes; and other valves M, M, adjoining to them in the top of each cylinder, opening inwards, but kept shut by a slight spring. Motion was given to the lever by a machine. The operation of this blowing machine is evident. When the cylinder A was pulled down, or allowed to descend, the water, entering at its bottom, compressed the air, and forced it along the passage FHIKT. In the mean time, the cylinder B was rising, and the air entered by the valve M. We see that the blast will be very unequal, increasing as the cylinder is immersed deeper. It is needless to describe this machine more particularly, because we shall give an account of one which we think per-

Pneumatic feet in its kind, and which leaves hardly any thing to be desired in a machine of this sort.

ABCD (fig. 98) is an iron cylinder, truly bored within, and

Fig. 98.

evasated a-top like a cup. EFGH is another, truly turned both without and within, and a small matter less than the inner diameter of the first cylinder. This cylinder is close above and hangs from the end of a lever moved by a machine. It is also loaded with weights at N. KLM is a third cylinder, whose outside diameter is somewhat less than the inside diameter of the second. This inner cylinder is fixed to the same bottom with the outer cylinder. The middle cylinder is loose, and can move up and down between the outer and inner cylinders without rubbing on either of them. The inner cylinder is perforated from top to bottom by three pipes OQ, SV, PR. The pipes OQ, PR have valves at their upper ends O, P, and communicate with the external air below. The pipe SV has a horizontal part VW, which again turns upwards, and has a valve at top X. This upright part WX is in the middle of a cistern of water fhkg. Into this cistern is fixed an air-chest a YZ b, open below, and having at top a pipe cde terminating in the tuyere at the furnace.

When the machine is at rest, the valves X, O, P, are shut by their own weights, and the air-chest is full of water. When things are in this state, the middle cylinder EFGH is drawn up by the machinery till its lower brims F and G are equal with the top KM of the inner cylinder. Now pour in water or oil between the outer and middle cylinders; and it will run down and fill the space between the outer and inner cylinders. Let it come to the top of the inner cylinder.

Now, let the loaded middle cylinder descend. It cannot do this without compressing the air which is between its top and the top of the inner cylinder. This air being compressed, will cause the water to descend between the inner and middle cylinders, and rise between the middle and outer cylinders, spreading into the cup; and as the middle cylinder advances downwards, the water will descend farther within it, and rise farther without it. When it has got so far down, and the air has been so much compressed, that the difference between the surface of the water on the inside and outside of this cylinder is greater than the depth of water between X and the surface of the water fg, air will go out by the pipe SVW, and will lodge in the air-chest, and will remain there if c be shut, which we shall suppose for the present. Pushing down the middle cylinder till the partition touch the top of the inner cylinder, all the air which was formerly between them will be forced into the air-chest, and will drive out water from it. Draw up the middle cylinder, and the external air will open the valves O, P, and again fill the space between the middle and inner cylinders; for the valve X will shut, and prevent the regress of the condensed air. By pushing down the middle cylinder a second time, more air will be forced into the air-chest, and it will at last escape by getting out between its brims Y, Z, and the bottom of the cistern; or if we open the passage e, it will pass along the conduit cde to the tuyere, and form a blast.

The operation of this machine is similar to Mr. Haskins's quicksilver pump, described by Desaguliers.1 The force which condenses the air is the load on the middle cylinder. The use of the water between the inner and outer cylinders, is to prevent this air from escaping; and the inner cylinder thus performs the office of a piston, having no friction. It is necessary that the length of the outer and middle cylinders be greater than the depth of the regulator-cistern, that there may be a sufficient height for the water to rise between the middle and outer cylinders, to balance the compressed air, and oblige it to go into the air-chest. A large blast-furnace will require the regulator-cistern five feet deep, and the cylinders about six or seven feet long.

It is in fact a pump without friction, and is perfectly air-tight. The quickness of its operation depends on the small space between the middle cylinder and the two others; and this is the only use of these two. Without these it would be similar to the engine at Chastillon, and operate more unequally and slowly. Its only imperfection is, that if the cylinder begin its motion of ascent or descent rapidly, as it will do when worked by a steam engine, there will be some danger of water dashing over the top of the inner cylinder, and getting into the pipe SV; but should this happen, an issue can easily be contrived for it at V, covered with a loaded valve e. This will never happen if the cylinder is moved by a crank. One blowing cylinder only is represented here, but two may be used.

We do not hesitate in recommending this form of bellows as the most perfect of any, and fit for all uses where standing bellows are required. They will be cheaper than any other sort for common purposes. For a common smith's forge they may be made with square wooden boxes instead of cylinders. They are also easily repaired. They are perfectly tight; and they may be made with a blast almost perfectly uniform, by making the cistern in which the air-chest stands, of considerable dimensions. When this is the case, the height of water, which regulates the blast, will vary very little.

This may suffice for an account of blast machines. The leading parts of their construction have been described as far only as was necessary for understanding their operation, and enabling an engineer to erect them in the most commodious manner. Views of complete machines might have amused, but they would not have added to our reader's information.

But the account is imperfect unless we show how their parts may be so proportioned that they shall perform what is expected from them. The engineer should know what size of bellows, and what load on the board or piston, and what size of tuyere, will give the blast which the service requires, and what force must be employed to give them the necessary degree of motion. We shall accomplish these purposes by considering the efflux of the compressed air through the tuyere. The propositions formerly delivered will enable us to ascertain this.

That we may proportion everything to the power employed, we must recollect, that if the piston of a cylinder employed for expelling air, be pressed down with any force p, it must be considered as superadded to the atmospheric pressure P on the same piston, in order that we may compare the velocity v of efflux with the known velocity V with which air rushes into a void. By what has been formerly delivered, it appears that this velocity \( v = V \times \sqrt{\frac{P}{P + p}} \).

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1 *Experimental Philosophy*, vol. ii. p. 491; and *Philosophical Transactions*, 1725, vol. xxxii. p. 3. Pneumatic where \( P \) is the pressure of the atmosphere on the piston, and \( p \) the additional load laid on it. This velocity is expressed in feet per second; and, when multiplied by the area of the orifice (also expressed in square feet) it will give us the cubical feet of condensed air expelled in a second; but the bellows are always to be filled again with common air, and therefore we want to know the quantity of common air which will be expelled; for it is this which determines the number of strokes which must be made in a minute, in order that the proper supply may be obtained. Therefore recollect that the quantity expelled from a given orifice with a given velocity, is in the proportion of the density; and that when \( D \) is the density of common air produced by the pressure \( P \), the density \( d \) produced by the pressure \( P + p \) is \( D \times \frac{P + p}{P} \); or if \( D \) be made 1, we have \( d = \frac{P + p}{P} \).

Therefore, calling the area of the orifice expressed in square feet \( O \), and the quantity of common air, or the cubic feet expelled in a second \( Q \), we have \( Q = V \times O \times \sqrt{\frac{P + p}{P}} \).

It will be sufficiently exact for all practical purposes, to suppose \( P \) to be 15 pounds on every square inch of the piston; and \( p \) is then conveniently expressed by the pounds of additional load on every square inch. We may also take \( V = 1332 \) feet.

As the orifice through which the air is expelled is generally very small, never exceeding three inches in diameter, it will be more convenient to express it in square inches; which being the \( \frac{1}{4} \) th of a square foot, we shall have the cubic feet of common air expelled in a second, or \( Q = \frac{1332}{144} \times \frac{O}{\sqrt{\frac{P + p}{P}}} \times \frac{P + p}{P} \).

This will perhaps be illustrated by taking an example in numbers. Let the area of the piston be four square feet, and the area of the round hole through which the air is expelled, be two inches, its diameter being 1.6, and let the load on the piston be 1728 pounds; this is three pounds on every square inch. We have \( P = 15 \), \( p = 3 \), \( P + p = 18 \), and \( O = 2 \); therefore we will have \( Q = 2 \times 9.25 \times \frac{\sqrt{3}}{18} \times \frac{18}{15} = 9.053 \) cubic feet of common air expelled in a second. This will however be diminished at least one-third by the contraction of the jet; and therefore the supply will not exceed six cubic feet per second. Supposing therefore that this blowing machine is a cylinder or prism of this dimension in its section, the piston so loaded would, after having compressed the air, descend about 15 inches in a second. It would first sink one-fifth of the whole length of the cylinder pretty suddenly, till it had reduced the air to the density \( \frac{1}{3} \), and would then descend uniformly at the above rate, expelling six cubic feet of common air in a second.

The computation is made much in the same way for bellows of the common form, with this additional circumstance, that as the loaded board moves round a hinge at one end, the pressure of the load must be calculated accordingly. The computation, however, becomes a little intricate, when the form of the loaded board is not rectangular. It is almost useless when the bellows have flexible sides, either like smith's bellows or like organ bellows, because the change of figure during their motion makes continual variation on the compressing powers. It is therefore chiefly with respect to the great wooden bellows, of which the upper board slides down between the sides, that the above calculation is of service.

The propriety, however, of this piece of information is evident: we do not know precisely the quantity of air necessary for animating a furnace; but this calculation tells us what force must be employed for expelling the air that may be thought necessary. If we have fixed on the strength of the blast, and the diameter of the cylinder, we learn the weight with which the piston must be loaded; the length of the cylinder determines its capacity, the above calculation tells the expense per second; hence we have the time of the piston's coming to the bottom. This gives us the number of strokes per minute. The load must be lifted up by the machine this number of times, making the time of ascent precisely equal to that of descent; otherwise the machine will either catch and stop the descent of the piston, or allow it to lie inactive for a while of each stroke. These circumstances determine the labour to be performed by the machine, and it must be constructed accordingly. Thus the engineer will not be affronted by its failure, nor will he expend needless power and cost.

In machines which force the piston or bellows board with a certain determined motion, different from what arises from their own weight, the computation is extremely intricate. When a piston moves by a crank, its motion at the beginning and end of each stroke is slow, and the compression and efflux is continually changing. We can however approximate to a statement of the force required.

Every time the piston is drawn up, a certain space of the cylinder is filled again with air of the common density; and this is expelled during the descent of the piston. A certain number of cubic feet of common air is therefore expelled with a velocity which perhaps continually varies; but there is a medium velocity with which it might have been uniformly expelled, and a pressure corresponding to this velocity. To find this, divide the area of the piston by the area of the blast-hole (or rather by this area multiplied by 0.613, in order to take in the effect of the contracted jet), and multiply the length of the stroke performed in a second by the quotient arising from this division; the product is the medium velocity of the air (of the natural density). Then find by calculation the height through which a heavy body must fall in order to acquire this velocity; this is the height of a column of homogeneous air which would expel it with this velocity. The weight of this column is the least force that can be exerted by the engine; but this force is too small to overcome the resistance in the middle of the stroke, and it is too great even for the end of the stroke, and much too great for the beginning of it. But if the machine is turned by a very heavy water-wheel, this will act as a regulator, accumulating in itself the superfluous force during the too favourable positions of the crank, and exerting it by its vis insita during the time of greatest effort. A force not greatly exceeding the weight of this column of air will therefore suffice. On the other hand, if the strength of the blast be determined, which is the general state of the problem, this determines the degree of condensation of the air, and the load on the square inch of the piston, or the mean force which the machine must exert on it. A table, which will be given presently, determines the cubic feet of common air expelled in a second, corresponding to this load. This combined with the proposed dimensions of the cylinder, will give the descent of the piston or the length of the stroke.

These general observations apply to all forms of bellows; and without a knowledge of them no person can erect a machine for working them without total uncertainty or servile imitation. In order, therefore, that they may be useful to such as are not accustomed to the management of even these simple formulas, we insert the following short table of the velocity and quantity of air discharged from a cylinder whose piston is loaded with the pounds contained in the first column on every square inch. The second column contains the velocity with which the condensed air Pneumatic rushes out through any small hole; and the third column is the cubic feet discharged from a hole whose area is a square inch; column fourth contains the mean velocity of air of the common density; and column fifth is the cubic feet of common air discharged; the sixth column is the height in inches at which the force of the blast would support a column of water if a pipe were inserted into the side of the cylinder. This is an extremely proper addition to such machines, showing at all times the power of the machines, and teaching us what intensity of blast is employed for different purposes. The table is computed from the supposition that the ordinary pressure of the air is 15 pounds on a square inch. This is somewhat too great, and therefore the velocities are a little too small; but the quantities discharged will be found about one-third too great, without affecting the velocities, on account of the convergency of the stream.

This table extends far beyond the limits of ordinary use, very few blast-furnaces having a force exceeding 60 inches of water.

We shall conclude this account of blowing machines with a description of a small one for a blow-pipe. (fig. 99) is a vessel containing water, about two feet deep. EFGH is the air-box of the blower open below, and having a pipe II.K rising up from it to a convenient height; an arm ON which grasps this pipe carries the lamp N; the blow-pipe LM comes from the top of the upright pipe. PKQ is the feeding-pipe reaching near to the bottom of the vessel.

Water being poured into the vessel below, and its cover being put on, which fits the upright pipe, and touches two studs a, a, projecting from it, blow in a quantity of air by the feeding pipe PQ; this expels the water from the air-box, and occasions a pressure which produces the blast through the blow-pipe M.

In a preceding part of this article, we mentioned an application which has been made of Hero's fountain, at Chemnitz in Hungary, for raising water from the bottom of a mine. We shall now give an account of this very ingenious contrivance.

In fig. 100, B represents the source of water elevated above the mouth of the pit 136 feet. From this there is led a pipe BCD, four inches diameter. This pipe enters the top of a copper cylinder c d e, 84 feet high, five feet diameter, and two inches thick, and it reaches to within four inches of the bottom; it has a cock at C. This cylinder has a cock at F, and a very large one at E. From the top CF proceeds a pipe GHI' two inches in diameter, which goes down the pit 96 feet, and is inserted into the top of another brass cylinder fgh i, which is 6½ feet high, four feet diameter, and two inches thick, containing 83 cubic feet, which is very nearly one-half of the capacity of the other, viz. of 170 cubic feet. There is another pipe NI of four inches diameter, which rises from within four inches of the bottom of this lower cylinder, soldered into its top, and rises to the trough NO, which carries off the water from the mouth of the pit. This lower cylinder communicates at the bottom with the water L which collects in the drains of the mine. A large cock K serves to admit or exclude this water; another cock M, at the top of this cylinder, communicates with the external air.

Now, suppose the cock C shut, and all the rest open; the upper cylinder will contain air, and the lower cylinder will be filled with water, because it is sunk so deep that its top is below the usual surface of the mine-waters. Now, shut the cocks F, E, M, K, and open the cock C. The water of the source B must run in by the orifice D, and rise in the upper cylinder, compressing the air above it and along the pipe GHI', and thus acting on the surface of the water in the lower cylinder. It will therefore cause it to rise gradually in the pipe IN, where it will always be of such a height that its weight balances the elasticity of the compressed air. Suppose no issue given to the air from the upper cylinder, it would be compressed into one-fifth of its bulk by the column of 136 feet high; for a column of 34 feet nearly balances the ordinary elasticity of the air. Therefore, when there is an issue given to it through the pipe GHI', it will drive the compressed air along this pipe, and it will expel water from the lower cylinder. When the upper cylinder is full of water, there will be 34 cubic feet of water expelled from the lower cylinder. If the pipe IN had been more than 136 feet long, the water would have risen 136 feet, being then in equilibrium with the water in the feeding pipe BCD, by the intervention of the elastic air; but no more water would have been expelled from the lower cylinder than what fills this pipe. But the pipe being only 96 feet high, the water will be thrown out at N with a very great velocity. If it were not for the great obstructions which water and air must meet with in their passage along pipes, it would issue at N with a velocity of more than 50 feet per second. It issues much more slowly, and at last the upper cylinder is full of water, and the water would enter the pipe GH and enter the lower cylinder, and without displacing the air in it, would rise through the discharging pipe IN, and run off to waste. To prevent this there hangs in the pipe HG a cork ball or double cone, by a brass wire which is guided by holes in two cross pieces in the pipe HG. When the upper cylinder is filled with water, this cork plugs up the orifice G; and no water is wasted; the influx at D now stops. But the lower cylinder contains compressed air, which would balance water in a discharging pipe 136 feet high, whereas IN is only 96. Therefore the water will continue to flow at N till the air has so far expanded as to balance only 96 feet of water, that is, till it occupies one-fourth of its ordinary bulk, that is, one-fourth of the capacity of the upper cylinder, or 42½ cubic feet. Therefore 42½ cubic feet will be expelled, and Pneumatic the efflux at N will cease; and the lower cylinder is about one-half full of water. When the attending workman observes this, he shuts the cock C. He might have done this before, had he known when the orifice G was stopped; but no loss ensues from the delay. At the same time the attendant opens the cock E, the water issues with great violence, being pressed by the condensed air from the lower cylinder. It therefore issues with the sum of its own weight and of this compression. These gradually decrease together, by the efflux of the water and the expansion of the air; but this efflux stops before all the water has flowed out; for there is 42½ feet of the lower cylinder occupied by air. This quantity of water remains, therefore, in the upper cylinder nearly; the workman knows this, because the discharged water is received first of all into a vessel containing three-fourths of the capacity of the upper cylinder. Whenever this is filled, the attendant opens the cock E by a long rod which goes down the shaft; this allows the water of the mine to fill the lower cylinder, allows the air to get into the upper cylinder, and this allows the remaining water to run out of it. And thus every thing is brought into its first condition; and when the attendant sees no more water come out at E, he shuts the cock E and M, and opens the cock C, and the operation is repeated.

There is a very surprising appearance in the working of this engine. When the efflux at N has stopped, if the cock F be opened, the water and air rush out together with prodigious violence, and the drops of water are changed into hail or lumps of ice. It is a sight usually shown to strangers, who are desired to hold their hats to receive the blast of air; the ice comes out with such violence as frequently to pierce the hat like a pistol bullet. This rapid congelation is a remarkable instance of the general fact, that air by suddenly expanding, generates cold, its capacity for heat being increased. Thus the peasant cools his broth by blowing over the spout, even from warm lungs; a stream of air from a pipe is always cooling.

The above account of the procedure in working this engine shows that the efflux both at N and E becomes very slow near the end. It is found convenient therefore not to wait for the complete discharges, but to turn the cocks when about 30 cubic feet of water have been discharged at N; more work is done in this way. A gentleman of great accuracy and knowledge of these subjects took the trouble, at our desire, of noticing particularly the performance of the machine. He observed that each stroke, as it may be called, took about three minutes and one-eighth; and that 32 cubic feet of water were discharged at N, and 66 were expended at E. The expense, therefore, is 66 feet of water falling 136 feet, and the performance is 32 raised 96, and they are in the proportion of $66 \times 136$ to $32 \times 96$, or of 1 to 0.3422, or nearly as 3 to 1. This is superior to the performance of the most perfect undershot mill, even when all friction and irregular obstructions are neglected, and is not much inferior to any overshot pump-mill that has yet been erected. When we reflect on the great obstructions which water meets with in its passage through long pipes, we may be assured that, by doubling the size of the feeder and discharger, the performance of the machine will be greatly improved; we do not hesitate to say, that it would be increased one-third: it is true that it will expend more water, but this will not be nearly in the same proportion, for most of the deficiency of the machine arises from the needless velocity of the first efflux at N. The discharging pipe ought to be 110 feet high, and not give sensibly less water. Then it must be considered how inferior in original expense this simple machine must be to a mill of any kind which would raise 10 cubic feet 96 feet high in a minute, and how small the repairs on it need be, when compared with a mill. And, lastly, let it be noticed, that such a Pneumatic machine can be used where no mill whatever can be put in motion. A small stream of water, which would not move any kind of wheel, will here raise one-third of its own quantity to the same height, working as fast as it is supplied.

For all these reasons, we think that the Hungarian machine eminently deserves the attention of mathematicians and engineers, to bring it to its utmost perfection, and into general use. There are situations where this kind of machine may be very useful. Thus, where the tide rises 17 feet, it may be used for compressing air to seven-eighths of its bulk; and a pipe leading from a very large vessel inverted in it, may be used for raising the water from a vessel of one-eighth of its capacity 17 feet high; or if this vessel has only one-tenth of the capacity of the large one set in the tide-way, two pipes may be led from it, one into the small vessel and the other into an equal vessel 16 feet higher, which receives the water from the first. Thus one-sixteenth of the water may be raised 34 feet, and a smaller quantity to a still greater height, and this with a kind of power that can hardly be applied in any other way. Machines of this kind are described by Schottus, Sturmius, Leupold, and other old writers; and they should not be forgotten, because opportunities may offer of making them highly useful. A gentleman's house in the country may thus be supplied with water by a machine that will cost little, and hardly go out of repair.

The last pneumatical engine which we shall speak of at present is the common fanners, used for winnowing grain, and for drawing air out of a room; and we have but few observations to make on them.

The wings of the fanners are enclosed in a cylinder or drum, whose circular sides have a large opening BDE (fig. 101), round the centre, to admit the air. By turning the wings rapidly round, the air is hurried round along with them, and thus acquires a centrifugal tendency, by which it presses strongly on the outer rim of the drum; this is gradually detached from the circle as at KI, and terminated in a trunk JHGF, which goes off in a tangential direction; the air therefore is driven along this passage.

If the wings were disposed in planes passing through the axis C, the compression of the air by the anterior surface would give it some tendency to escape in every direction, and would obstruct in some degree the arrival of more air through the side holes. They are therefore reclined a little backward, as represented in the figure. It may be shown that their best form would be that of a hyperbolic spiral abcf; but the straight form approaches sufficiently near to the most perfect shape.

Much labour is lost, however, in carrying the air round those parts of the drum where it cannot escape. The fanners would either draw or discharge almost twice as much air if an opening were made all round one side. This could be gradually contracted, where required for winnowing, by a surrounding cone, and thus directed against the falling grain; as has been verified by actual trial. When used for drawing air out of a room for ventilation, it would be much better to remove the outer side of the drum entirely, and let the air fly freely off on all sides; but the flat sides are necessary, in order to prevent the air from arriving at the fanners any other way but through the central holes, to which trunks should be fitted leading to the apartment which is to be ventilated.