(from baro weight, and metron measure), an instrument for measuring the weight of the atmosphere, and of use in foretelling the changes of the weather, and also for measuring the height of mountains, &c.

The common barometer consists of a glass tube hermetically sealed at one end, and filled with quicksilver well dejected and purged of its air. The finger being then placed on the open end, in immediate contact with the mercury, so as not to admit the least particle of air, the tube is inverted, and the lower end plunged into a basin of the same prepared mercury; then, upon removing the finger, the mercury in the tube will join that in the basin, and the mercurial column in the tube will subside to the height of 29 or 30 inches, according to the state of the atmosphere at that time. This is the principle on which all barometers are constructed. Of their invention, the different kinds of them, and the theories by which their phenomena are solved, we shall proceed to give an historical account.

In the beginning of the last century, when the doctrine of a plenum was in vogue, philosophers were of opinion, that the ascent of water in pumps was owing to the abhorrence of a vacuum; and that, by means of suction, fluids might be raised to any height whatever. But Galileo, who flourished about that time, discovered that water would not ascend in a pump unless the sucker reached within 33 feet of its surface in the well. From hence he concluded, that not the power of suction, but the pressure of the atmosphere was the cause of the ascent of water in pumps; that a column of water 33 feet high was a counterpoise to one of air of an equal base, whose height extended to the top of the atmosphere; and that for this reason the water would not follow the sucker any farther. From this Torricelli, Galileo's disciple, took the hint; and considered, that if a column of water of about 33 feet in height was equal in weight to one of air having the same base; a column of mercury no longer than about 29½ inches would be too short, because mercury being about 14 times heavier than water, a column of mercury must be 14 times shorter than one of water equally heavy. Accordingly, having filled a glass tube with mercury, and inverted it into a basin of the same, he found the mercury in the tube to descend till it stood about 29½ inches above the surface of that in the basin.

Notwithstanding this clear proof of the pressure of the atmosphere, however, the assertors of a plenum left no means untried to solve the phenomena of the Torricellian experiment by some other hypothesis. The most ridiculous solution, and which at the same time gave the adverse party the greatest difficulty to overthrow it, was that of Linus. He contended, that, in the upper part of the tube, there is a film, or rope of mercury, extended through the seeming vacuity; and that, by this rope, the rest of the mercury was suspended, and kept from falling into the basin. Even this so absurd hypothesis he pretended to confirm by the following experiments. Take, says he, a small tube, open at both ends, suppose about 20 inches long; fill this tube with mercury, stopping the lower orifice with your thumb: Then clotting the upper end with your finger, and immersing the lower end in flagrant mercury, you shall perceive, upon the removal of your thumb, a manifest suction of your finger into the tube; and the tube and mercury will both stick so close to it, that you may carry them about the room. Therefore, says he, the internal cylinder of mercury in the tube is not held up by the preponderant air without; for if so, whence comes so strong a suction, and so firm an adhesion of the tube to the finger?—The same effect follows, though the tube be not quite filled with mercury; for if a little space of air is left at the top, after the tube is immersed in the flagrant mercury, there will be a considerable suction as before.

These experiments, which are themselves clear proofs of the pressure of the air, supported for some time the funicular hypothesis, as it was called, of Linus. But when it was discovered, that if the tube was carried to the top of an high mountain the mercury stood lower than on the plain, and that if removed into the vacuum of an air-pump it fell out altogether, the hypothesis of Linus was rejected by every body.—There are, however, two experiments which create a considerable difficulty. One is mentioned by Mr. Huygens, viz. that if a glass tube 75 inches long, or perhaps longer, is filled with mercury well purged of its air, and then inverted, the whole will remain suspended; whereas, according to the Torricellian experiment, it ought to subside immediately to the height of 29 or 30 inches. It is true indeed, that, upon shaking the tube, the mercury presently subsides to that height; but why it should remain suspended at all, more than twice the height to which it can be raised by the pressure of the most dense atmosphere, seems not easily accounted for; and accordingly, in the Philosophical Transactions, we find unsatisfactory attempts to account for it by the pressure of a medium more subtle than the common air, and capable of pervading both the mercury and glass. We find there also another very surprising fact of the same kind mentioned; viz. that a pretty large tube under 29 inches in length, filled with mercury, and inverted into a basin of the same, will remain full, though there be a small hole in the top. This, too, is there accounted for by the pressure of a medium more subtle than common air; but by no means in a satisfactory manner. Mr. Rowning, who mentions the phenomenon of the 75 inch Mr. Rowning tube, accounts for it in the following manner. "The thing's sole cause of this phenomenon seems to be, that by the great weight of so long a column of mercury, it was pressed into so close contact with the glass in pouring in, that, by the mutual attraction of cohesion between the mercury and the glass, the whole column was sustained after the tube was inverted."—Here, however, we must observe, that this solution seems equally unsatisfactory with that of the subtle medium already mentioned; because it is only one end of the column which sustains so great a pressure from the weight of the mercury; and therefore, though five or six inches of the upper part of the tube, where the pressure had been strongest, might thus remain full of mercury, yet the rest ought to fall down. Besides, it is only the outside of the mercurial column that is in contact with the glass, and consequently these parts only ought to be attracted. Therefore, even granting the pressure to be equally violent, on the inversion of the tube, all the way from 29 to 75 inches, yet the glass ought to be only as it were silvered over by a very thin film of mercury, while the middle parts of the column ought to fall out by reason of their fluidity.

The other experiment hinted at, is with regard to siphons; which though it belongs more properly to the article HYDRAULICS, yet seems necessary to be mentioned here. It is this: That a siphon, once set running, will continue to do so though set under the receiver of an air-pump and the air exhausted in the most perfect manner; or if a siphon is filled, and then set under a receiver and the air exhausted, if by any contrivance the end of the lower leg is opened, it will immediately begin to run, and discharge the water of any vessel in which the other leg is placed, as though it was in the open air. The cause of this phenomenon, as well as the former, seems very difficult to be investigated.

In Chambers's Dictionary, under the word Siphon, we have a solution something similar to the famous hypothesis of Linus abovementioned; namely, that "fluids in siphons seem as if they were to form one continued body; so that the heavier part, descending, like a chain pulls the lighter after it." This might be deemed a sufficient explication, if the siphon was only to empty the water it at first contains in itself; but when we consider that the water in the vessel, which much exceeds the quantity contained in the siphon, is likewise evacuated, Mr. Chambers's hypothesis can by no means be admitted; because this would be like the lighter part of a chain pulling the heavier after it.

Concerning the cause of these singular phenomena, we can only offer the following conjecture. The existence of a medium much more subtle than air, and which pervades the vacuum of an air-pump with the utmost facility, is now sufficiently ascertained in the phenomena of electricity. It is also well known, that this fluid surrounds the whole earth to an indeterminate height. If therefore this fluid either is the power of gravity itself, or is acted upon by that power, it must necessarily press upon all terrestrial bodies in a manner similar to the pressure of the atmosphere. If then we could from any vessel entirely exclude this subtle fluid, and form an electrical vacuum, as well as we can do an aerial one by means of the air-pump, we would in that case see fluids as evidently raised by the pressure of the electric matter, as we now see them raised by that of the air. But the this cannot be done, we are assured that there are certain substances, of which glass is one, through which the electric matter cannot pass but with difficulty. We are likewise certain, that tho' the electric matter passes through the pores of water, metals, &c. with very great facility, yet it still must meet with some resistance from their solid and impermeable parts, which cannot be pervaded by any material substance. We know also, that all substances do naturally contain a certain quantity of this electric matter, which they are not always ready to part with; and when by any means the fluid they contain is set in motion, they are then said to be electrified. Now, though we are certain, that the friction of glass by mercury does set in motion the electric fluid contained in the mercury, or in the glass; yet, when the tube is filled with the metallic fluid, whatever quantity has been extricated, either from the glass or mercury, during the time of filling, will be reabsorbed by the metal, and conveyed to the earth, during the time of inversion; and consequently the mercurial tube, when inverted, will not be electrified, but both glass and mercury will be in their natural state. Here, then, the pressure of the electrical fluid is kept off in some measure from the upper part of the mercury by the glass, which it cannot penetrate, easily at least. To the mercury in the basin it has free access, and therefore presses more upon the lower than the upper part; the consequence of which is a suspension of the mercury. It is true, this fluid very easily penetrates the metallic matter; but it must be considered, that the electric fluid itself is in some measure entangled in the particles of the quicksilver, and cannot be extricated without motion. As soon therefore as the tube is shaken, some part of the electricity is extricated, and the mercury begins to descend. The subtlety of the medium is such, that no sooner has it begun to extricate itself, than, by the motion of the metal downwards, it issues forth in great quantities, so as to become visible, like a blue flame, in the dark. The equilibrium is therefore destroyed in an instant, as it would be were we to admit air to the top of the barometer; nay, in a more effectual manner. For if a small quantity of air was admitted to the top of a barometer, the mercury would only descend in proportion to the quantity of air admitted; but here, no sooner is a quantity of electric matter admitted, than it procures admission for a vast deal more, and consequently the mercury descends with accelerated velocity.—On this principle the ascent of water in the siphon while in vacuo is so easily accounted for, that we need not take up time in explaining it farther.—But why an inverted glass tube should remain full of mercury when it has a hole either great or small in the top, is more difficult to be accounted for, and requires this farther circumstance to be taken into consideration, viz. that though all solid bodies will, by the action of gravity, or by any other impulse, easily approach very near to one another, yet they cannot be brought into absolute contact without a very considerable force, much greater than is sufficient to overcome their gravity; and thus it appears from some experiments, that the links of a chain are by no means in contact with one another, till the chain has a considerable weight appended to it. This may be the case with the tube in question. The air by its gravity descends upon it, and is ready to enter the small hole in the top; but, by a repulsive power from the glass, its action is prevented, so that the mercury cannot fall.

It was, however, some time after the Torricellian experiment had been made, and even after it had been universally agreed that the suspension of the mercury was owing to the weight of the atmosphere, before it was discovered that this pressure of the air was different at different times though the tube was kept in the same place. But the variations of altitude in the mercurial column were too obvious to remain long unobserved; and accordingly philosophers soon became careful When this was done, it was impossible to avoid observing also, that the changes in the height of the mercury were accompanied, or very quickly succeeded, by changes in the weather. Hence the instrument obtained the name of the weather-glass, and was generally made use of with a view to the foreknowledge of the weather. In this character, its principal phenomena are as follow:

1. The rising of the mercury presages, in general, fair weather; and its falling, foul weather, as rain, snow, high winds, and storms.

2. In very hot weather, the falling of the mercury forebodes thunder.

3. In winter, the rising presages frost; and in frosty weather, if the mercury falls three or four divisions, there will certainly follow a thaw. But in a continued frost, if the mercury rises, it will certainly snow.

4. When foul weather happens soon after the falling of the mercury, expect but little of it; and, on the contrary, expect but little fair weather when it proves fair shortly after the mercury has risen.

5. In foul weather, when the mercury rises much and high, and so continues for two or three days before the foul weather is quite over, then expect a continuance of fair weather to follow.

6. In fair weather, when the mercury falls much and low, and thus continues for two or three days before the rain comes; then expect a great deal of wet, and probably high winds.

7. The unsettled motion of the mercury denotes uncertain and changeable weather.

8. You are not to strictly to observe the words engraved on the plates, (though in general it will agree with them) as the mercury's rising and falling. For if it stands at much rain, and then rises up to changeable, it presages fair weather; though not to continue so long as if the mercury had risen higher; and so, on the contrary, if the mercury stood at fair, and falls to changeable, it presages foul weather; though not so much of it as if it had sunk lower.

These are the observations of Mr Patrick, on which Mr Rowning makes the following remarks. "From these observations it appears, That it is not so much the height of the mercury in the tube, that indicates the weather, as the motion of it up and down: wherefore, in order to pass a right judgment of what weather is to be expected, we ought to know whether the mercury is actually rising or falling; to which end the following rules are of use.

1. If the surface of the mercury is convex, standing higher in the middle of the tube than at the sides, it is generally a sign that the mercury is then rising.

2. If the surface is concave, it is then sinking; and,

3. If it is plain, the mercury is stationary, or rather if it is a little convex; for mercury being put into a glass tube, especially a small one, will naturally have its surface a little convex, because the particles of mercury attract one another more forcibly than they are attracted by glass. Further,

4. If the glass is small, shake the tube; and if the air is grown heavier, the mercury will rise about half the tenth of an inch higher than it stood before; if it is grown lighter, it will sink as much. This proceeds from the mercury's sticking to the sides of the tube, which prevents the free motion of it till it is disengaged by the shock: and therefore, when an observation is to be made with such a tube, it ought always to be shaken first; for sometimes the mercury will not vary of its own accord, till the weather it ought to have indicated is present."

Here we must observe, that the abovementioned phenomena are peculiar to places lying at a considerable distance from the equator; for, in the torrid zone, the mercury in the barometer seldom either rises or falls much. In Jamaica, it is observed by Sir William Beechey*, that the mercury in the morning constantly stood at one degree below changeable; and at noon sunk to one degree above rain; so that the whole scale of variation there was only ¼ of an inch. At St Helena, too, where Dr Halley made his observations, he found the mercury to remain mostly stationary whatever weather happened. Of these phenomena, their causes, and why the barometer indicates an approaching change of weather, the Doctor gives us the following account.

"1. In calm weather, when the air is inclined to rain, the mercury is commonly low.

"2. In serene, good, and settled weather, the mercury is generally high.

"3. Upon very great winds, though they be not accompanied with rain, the mercury sinks lowest of all, with relation to the point of the compass the wind blows upon.

"4. Ceteris paribus, the greatest heights of the mercury are found upon easterly, or north-easterly winds.

"5. In calm frosty weather, the mercury generally stands high.

"6. After very great storms of wind, when the mercury has been very low, it generally rises again very fast.

"7. The more northerly places have greater alterations of the barometer than the more southerly.

"8. Within the tropics, and near them, those accounts we have had from others, and my own observations at St Helena, make very little or no variation of the height of the mercury in all weathers.

"Hence I conceive that the principal cause of the rise and fall of the mercury is from the variable winds which are found in the temperate zone, and whose great inconstancy, here in England, is notorious.

"A second cause is, the uncertain exhalation and precipitation of the vapours lodging in the air, whereby it comes to be at one time much more crowded than at another, and consequently heavier; but this latter depends in a great measure upon the former. Now from these principles I shall endeavour to explicate the several phenomena of the barometer, taking them in the same order I have laid them down. Thus,

"1. The mercury's being low inclines it to rain, because the air being light, the vapours are no longer supported thereby, being become specifically heavier than the medium wherein they floated; so that they descend towards the earth, and, in their fall, meeting with other aqueous particles, they incorporate together, and form little drops of rain; but the mercury's being at one time lower than another, is the effect of two contrary winds blowing from the place where the barometer stands; whereby the air of that place is carried both ways from it, and consequently the incumbent cylinder of air is diminished, and accordingly the mercury sinks: As, for instance, if in the German ocean it should blow a gale of westerly wind, and, at the same time, an easterly wind in the Irish Sea; or, if in France it should blow a northerly wind, and in Scotland a southerly; it must be granted, that that part of the atmosphere impendant over England would thereby be exhausted and attenuated, and the mercury would subside, and the vapours which before floated in these parts of the air of equal gravity with themselves would sink to the earth.

2. The greater height of the barometer is occasioned by two contrary winds blowing towards the place of observation, whereby the air of other places is brought thither and accumulated; so that the incumbent cylinder of air being increased both in height and weight, the mercury pressed thereby must needs stand high, as long as the winds continue to blow; and then the air being specifically heavier, the vapours are better kept suspended, so that they have no inclination to precipitate and fall down in drops, which is the reason of the serene good weather which attends the greater heights of the mercury.

3. The mercury sinks the lowest of all by the very rapid motion of the air in storms of winds. For the tract or region of the earth's surface, wherein the winds rage, not extending all round the globe, that stagnant air which is left behind, as likewise that on the sides, cannot come in so fast as to supply the evacuation made by so swift a current, so that the air must necessarily be attenuated, when and where the said winds continue to blow, and that more or less according to their violence: add to which, that the horizontal motion of the air being so quick as it is, may in all probability take off some part of the perpendicular pressure thereof; and the great agitation of its particles is the reason why the vapours are dilated, and do not condense into drops so as to form rain, otherwise the natural consequence of the air's rarefaction.

4. The mercury stands highest upon the easterly and north-easterly wind; because in the great Atlantic ocean, on this side the 35th degree of north latitude, the winds are almost always westerly or south-westerly; so that whenever here the wind comes up at east and north-east, it is sure to be checked by a contrary gale as soon as it reaches the ocean; wherefore, according to our second remark, the air must needs be heaped over this island, and consequently the mercury must stand high, as often as these winds blow. This holds true in this country; but is not a general rule for others, where the winds are under different circumstances: and I have sometimes seen the mercury here as low as 29 inches upon an easterly wind; but then it blew exceedingly hard, and so comes to be accounted for by what was observed in the third remark.

5. In calm frosty weather the mercury generally stands high; because (as I conceive) it seldom freezes but when the winds come out of the northern and north-easterly quarters: or at least, unless those winds blow at no great distance off. For the north parts of Germany, Denmark, Sweden, Norway, and all that tract from whence north-easterly winds come, are subject to almost continual frost all the winter: and thereby the lower air is very much condensed, and in that state is brought hitherward by those winds, and, being accumulated by the opposition of the westerly wind blowing in the ocean, the mercury must needs be pressed to a more than ordinary height; and as a concurring cause, the shrinking of the lower parts of the air into lesser room by cold, must needs cause a descent of the upper parts of the atmosphere, to reduce the cavity made by this contraction to an equilibrium.

6. After great storms, when the mercury has been very low, it generally rises again very fast: I once observed it to rise one inch and an half in less than six hours after a long continued storm of south-west wind. The reason is, because the air being very much rarefied by the great evacuations which such continued storms make thereof, the neighbouring air runs in the more swiftly to bring it to an equilibrium; as we see water runs the faster for having a greater declivity.

7. The variations are greater in the more northerly places, as at Stockholm greater than at Paris (compared by M Pafchal); because the more northerly parts have usually greater storms of wind than the more southerly, whereby the mercury should sink lower in that extreme; and then the northerly winds bringing in the more dense and ponderous air from the neighbourhood of the pole, and that again being checked by a southerly wind at no great distance, and so heaped, must of necessity make the mercury in such case stand higher in the other extreme.

8. Lastly, this remark, that there is little or no variation near the equinoctial, does above all others confirm the hypothesis of the variable winds being the cause of these variations of the height of the mercury; for in the places above named, there is always an easy gale of wind blowing nearly upon the same point, viz. E. N. E. at Barbadoes, and E. S. E. at St. Helena; so that there being no contrary currents of air to exhaust or accumulate it, the atmosphere continues much in the same state: however, upon hurricanes, the most violent of storms, the mercury has been observed very low; but this is but once in two or three years, and it soon recovers its settled state, about 29½ inches."

This theory we find controverted by Mr Chambers, Objecting in his Dictionary under the word Barometer. The principal objections are, That if the wind was the sole agent in raising or depressing the mercury, the alterations of its height in the barometer would be only relative or topical; there would still be the same quantity supported at several places taken collectively: thus what a tube at London lost, another at Paris, Pifa, or Zurich, &c. would gain. But the contrary is found to be the case; for, from all the observations hitherto made, the barometers in several distant parts of the globe rise and fall together. This is a very surprising fact; and deserves to be well examined. Again, setting aside all other objections, it is impossible, on Dr Halley's hypothesis, to explain the mercury's fall before, and rise after, rain. For suppose two contrary winds sweeping the air from over London; we know that few if any of the winds reach above a mile high; all therefore they can do will be to cut off a certain part of the column of air over London: if the consequence of this be the fall of the mercury, yet there is no apparent reason for the rains following it. The vapours indeed may be let lower; but it will only be till they come into an air of the same specific gravity with themselves, and there they will stick as before. Lastly, it Mr Leibnitz accounted for the sinking of the mercury before rain upon another principle, viz. That as a body specifically lighter than a fluid, while it is suspended by it, adds more weight to that fluid, than when, by being reduced in its bulk, it becomes specifically heavier, and descends; so the vapour, after it is reduced into the form of clouds, and descends, adds less weight to the air than before; and therefore the mercury falls. To which it is answered, 1. That when a body descends in a fluid, its motion in a very little time becomes uniform, or nearly so, a farther acceleration of it being prevented by the resistance of the fluid; and then, by the third law of nature, it forces the fluid downwards with a force equal to that whereby it tends to be farther accelerated, that is, with a force equal to its whole weight. 2. The mercury by its descent foretells rain a much longer time before it comes, than the vapour after it is condensed into clouds can be supposed to take up in falling.

3. Supposing that as many vapours as fall in rain during a whole year were at once to be condensed into clouds, and even quite cease to gravitate upon the air, its gravity would scarce be diminished thereby so much as is equivalent to the descent of two inches of mercury in the barometer. Besides, in many places between the tropics, the rains fall at certain seasons in very great quantities, and yet the barometer shows there very little or no alteration in the weight of the atmosphere.

Mr Chambers gives an hypothesis somewhat similar to that of Leibnitz; but as it is liable to the objections just now mentioned, especially the last, we forbear to give any particular account of it; and shall attempt, upon other principles, to give a satisfactory solution of this phenomenon.

The necessary preliminaries to our hypothesis are,

1. That vapour is formed by an intimate union between the element of fire and that of water, by which the fire or heat is so totally enveloped, and its action so entirely subserved by the watery particles, that it not only loses its properties of giving light and burning, but becomes incapable of affecting the most sensible thermometer; in which case, it is said by Dr Black, the author of this theory, to be in a latent state. For the proofs of this, see the articles Evaporation, Cold, Congelation, &c.

2. If the atmosphere is affected by any unusual degree of heat, it thence becomes incapable of supporting so long a column of mercury as before, for which reason that in the barometer sinks. This appears from the observations of Sir William Beeleton already mentioned; and likewise from those of De Luc, which shall be afterwards taken notice of.

These axioms being established, it thence follows, that as vapour is formed by an union of fire with water, or if we please to call it an elective attraction between them, or cohesion of the water in the fire, it is impossible that the vapour can be condensed until this union, attraction, or cohesion, be at an end. The beginning of the condensation of the vapour then, or the first symptoms of an approaching rain, must be the separation of the fire which lies hid in the vapour. This may be at first slow and partial, or it may be sudden and violent; in the first case, the rain will come on slowly, and after a considerable interval; and in the other, it will be very quick, and in great quantity.

But Dr Black hath proved, that when fire quits its latent state, however long it may have lain dormant and insensible, it always assumes its proper qualities again, and affects the thermometer as though it had never been absorbed. The consequence of this must be, that in proportion as the latent heat is discharged from the vapour, it must sensibly affect those parts of the atmosphere into which it is discharged; and in proportion to the heat communicated to these, they will become specifically lighter, and the mercury sink of course. Neither are we to imagine that the quantity of heat discharged by the vapour is inconsiderable; for Dr Black hath shewn, that when any quantity of water, a pound for instance, is condensed from the vapour of a common still, as much heat is communicated to the head and refrigeratory as would have been insufficient to heat the pound of water red hot, could it have born that degree of sensible heat.

The causes by which this separation between the fire and water is, or may be, effected, come to be considered under the articles Rain, Condensation, Vapour, &c. Here we have only to observe, that as the separation may be gradual and slow, the barometer may indicate rain for a considerable time before it happens; or if the sensible heat communicated from the vapour to the atmosphere shall be absorbed by the colder parts, or by any unknown means carried off, or prevented from affecting the specific gravity of the air, the barometer will not be affected; and yet the water being deprived of the heat necessary to sustain it, must descend in rain; and thus it is found that the indications of the barometer do not always hold true. Hence also it appears, that tho' the specific gravity of the air is diminished, unless that diminution proceeds from a discharge of the latent heat contained in the vapours, no rain will follow; and thus the sinking of the barometer may prognosticate wind as well as rain, or sometimes nothing at all.

The difficulty, however, on this hypothesis, is to account for the barometer being stationary in all weathers between the tropics; whereas it ought to move up and down there as well as here, only more suddenly, as the changes of weather there are more sudden than here. But it must be considered, that in these climates, during the day-time, the action of the sun's rays is so violent, that what is gained by the discharge of latent heat from the vapour, is lost by the interposition of the clouds betwixt the sun and earth; and in the night, the cold of the atmosphere is so much increased, that it absorbs the heat as fast as the vapour discharges it, so that no sensible effect can be produced; for in warm climates, tho' the day is excessively hot, the night is observed to be vastly colder in proportion than it is with us. This, however, does not prevent the barometer from being affected by other causes, as well as with us; for Dr Halley observes, that in the time of Having thus given an account of the several phenomena of the barometer considered as a weather-glass, and likewise endeavoured to account for them in the most satisfactory manner, we now proceed to give a particular description of the barometers most commonly made use of, with various schemes for their improvement.

Fig. V. No. 1 represents the common barometer, such as was invented by Torricelli; and such as we have already given a general description of. AB represents a tube of glass, a quarter of an inch in diameter, and 34 inches long, hermetically sealed at A. This tube being supposed to be filled with mercury, is then inverted into the basin CD; upon which the mercury in the tube falls down to GH, somewhat above 28 inches, while that in the basin rises to CF. The lowest station of the mercury in this country is found to be 28 inches, and the highest 31. From the surface of the mercury CF, therefore, 28 inches are to be measured on the tube AB, which suppose to reach to the point K. This point, therefore, is the lowest of the scale of variation, and in the common barometers is marked **storm**. In like manner, the highest point of the scale of variation I, is placed 31 inches above EF; and is marked **very dry** on one side for the summer, and **very hard frost** on the other for the winter. The next half inch below is marked **set fair** on the one side, and **set fresh** on the other. At 30 inches from CF is marked the word **fair** on one side, and **fresh** on the other. Half an inch below that, is wrote the word **changeable**, which answers both for summer and winter. At 29 inches is **rain** on the one side, and **snow** on the other; and at 28½, are the words **much rain** on the one side, and **much snow** on the other. Each of these large divisions is usually subdivided into ten; and there is a small sliding index fitted to the instrument, by which the ascent or descent of the mercury to any number of divisions is pointed out.

This kind of barometer is the most common, and perhaps the most useful of any that hath yet been invented; but as the scale of variation here is only three inches, and it is naturally wished to discover more minute variations than can thus be perceived, several improvements have been thought of.

The improvement most generally adopted is the diagonal barometer represented No. 2, in which the scale of variation, instead of three inches, may be made as many feet, by bending the tube so as to make the upper part of it the diagonal of a parallelogram of which the shortest side is the three-inches scale of variation of the common barometer. This, however, has a very great inconvenience: for not only is the friction of the mercury upon the glass so much increased that the height doth not vary with every flight change of air; but the column of mercury is apt to break in the tube, and part of it to be left behind, upon any considerable descent.

No. 3. is the rectangular barometer; where AC represents a pretty wide cylinder of glass, from which proceeds the tube CDF bent into a right angle at D. Suppose now the cylinder AC to be four times larger than the tube CD, so that every inch of the cylinder from C to A should be equal in capacity to four inches of the tube CD. The whole being then filled with mercury, and inverted, the mercury will subside from A to B, at the same time that it cannot run out at the open orifice F, because the air presses in that way. If any alteration then happens in the weight of the air, suppose such as would be sufficient to raise the mercury an inch from B towards A, it is evident that this could not be done without the mercury in the horizontal leg retiring four inches from E towards D; and thus the scale of variation counted on the horizontal leg would be 12 inches. But the inconveniences of friction are much greater here than in the diagonal barometer; and besides, by the leak accident the mercury is apt to be driven out at the open orifice F.

The pendant barometer (No. 4) consists of a single tube, suspended by a string fastened to the end A. This tube is of a conical or tapering figure, the end A being somewhat less than the end B. It is hermetically sealed at A, and filled with mercury: then will the mercury sink to its common station, and admit of a length of altitude CD, equal to that in the common barometers. But from the conical bore of the tube the mercury will descend as the air grows lighter, till it reaches its lowest altitude, when the mercury will stand from the lower part of the tube B to E, so that BE will be equal to 28 inches: consequently the mercury will, in such a tube, move from A to E, or 32 inches, if the tube be five feet, or 60 inches; and therefore the scale AE is here above ten times greater than in the common barometer: but the fault of this barometer is, that the tube being of a very small bore, the friction will be considerable, and prevent its moving freely; and if the tube is made of a wider bore, the mercury will be apt to fall out.

No. 5. is an invention of Mr Rowning, by which the scale of variation may be increased to any length, or even become infinite. ABC is a compound tube hermetically sealed at A, and open at C; empty from A to D, filled with mercury from thence to B, and from thence to E with water. Let GBH be a horizontal line; then it is plain from the nature of the syphon, that all the compound fluid contained in the part from H to G, will be always in equilibrium with itself; be the weight of the air what it will, because the pressure at H and G must be equal. Whence it is evident, that the column of mercury DH is in equilibrium with the column of water GE, and a column of air taken conjointly, and will therefore vary with the sum of the variations of these. That the variation in this barometer may be infinite, will appear from the following computation. Let the proportion between the bores of the tube AF and FC be such, that when HD, the difference of the legs wherein the mercury is contained, is augmented one inch, GE, the difference of the legs wherein the water is contained, shall be diminished 1¼; then, as much as the pressure of the mercury is augmented, that of the water will be diminished, and so the pressure of both taken together will remain as it was; and consequently, after it has begun to rise, it will have the same tendency to rise on, without ever coming to an equilibrium with the air.

No. 6. represents Dr Hook's wheel-barometer. Here ACDG is a glass tube, having a large round head at A, and turned up at the lower end F. Upon the surface of the mercury in the bent leg is an iron ball G, with a string going over a pulley CD. To the other end of the string is fastened a smaller ball H, which as the mercury rises in the leg FG, turns the index KL from N towards M, on the graduated circle MNOP; as it rises in the other legs, the index is carried the contrary way by the descent of the heavier ball G, along with the mercury. The friction of this machine, however, unless it is made with very great accuracy, renders it useless.

No. 7, is another barometer invented by Mr Rowning, in which also the scale may be infinite. ABCD is a cylindrical vessel, filled with a fluid to the height W, in which is immersed the barometer SP consisting of the following parts: The principal one is the glass tube TP, (represented separately at m), whose upper end T is hermetically sealed; this end does not appear to the eye, being received into the lower end of a tin pipe GH, which in its other end G receives a cylindrical rod or tube ST, and thus fixes it to the tube TP. This rod ST may be taken off, in order to put in its stead a larger or a lesser as occasion requires. S is a star at the top of the rod ST; and serves as an index by pointing to the graduated scale LA, which is fixed to the cover of the vessel ABCD. MN is a large cylindrical tube made of tin, (represented separately at m), which receives in its cavity the smaller part of the tube TP, and is well cemented to it at both ends, that none of the fluid may get in. The tube TP, with this apparatus, being filled with mercury, and plunged into the basin MP, which hangs by two or more wires upon the lower end of the tube MN, must be so poised as to float in the liquor contained in the vessel ABCD; and then the whole machine rises when the atmosphere becomes lighter, and vice versa. Let it now be supposed, that the fluid made use of is water; that the given variation in the weight of the atmosphere is such, that, by pressing upon the surface of the water at W, the surface of the mercury at X may be raised an inch higher, (measuring from its surface at P), than before; and that the breadth of the cavity of the tube at X, and of the basin at P, are such, that, by this ascent of the mercury, there may be a cubic inch of it in the cavity X more than before, and consequently in the basin a cubic inch less. Now, upon this supposition, there will be a cubic inch of water in the basin more than there was before; because the water will succeed the mercury, to fill up its place. Upon this account the whole machine will be rendered heavier than before by the weight of a cubic inch of water; and therefore will sink, according to the laws of hydrostatics, till a cubic inch of that part of the rod WS, which was above the surface of the water at W, comes under it. Then, if we suppose this rod so small, that a cubic inch of it shall be 14 inches in length, the whole machine will sink 14 inches lower into the fluid than before; and consequently the surface of the mercury in the basin will be preëlevated, more than it was before, by a column of water 14 inches high. But the pressure of 14 inches of water is equivalent to one of mercury; this additional pressure will make the mercury ascend at X as much as the supposed variation in the weight of the air did at first. This ascent will give room for a second cubic inch of water to enter the basin; the machine will therefore be again rendered so much heavier, and will subside 14 inches farther, and so on in infinitum. If the rod was so small that more than fourteen inches of it were required to make a cubic inch, the variation of this machine would be negative with respect to the common barometer; and instead of coming nearer to an equilibrium with the air by its ascent or descent, it would continually recede farther from it; but if less than 14 inches of rod were required to make a cubic inch, the scale of variation would be finite, and might be made in any proportion to the common one. Neither this nor the other infinite barometer have ever been tried, so that how far they would answer the purposes of a barometer is as yet unknown.

No. 8 represents another contrivance for enlarging the scale of the barometer to any size.—AB is the tube of a common barometer open at B and sealed at A, suspended at the end of the lever which moves on the fulcrum E.—CD is a stiff glass tube, which serves in place of the cistern. This last tube must be so wide as to allow the tube AB to play up and down within it.—AB being filled with mercury, is nearly counterbalanced by the long end of the lever. When the atmosphere becomes lighter, the mercury descends in the long tube, and the surface of the mercury rising in the cistern pushes up the tube AB, which at the same time becoming lighter, the lever preponderates, and points out the most minute variations. Here too the friction occasions inconveniences; but this may be in some measure remedied by a small shake of the apparatus at each inspection.

In the Philosophical Transactions, Mr Cawell gives the following account of a barometer, which is recommended by Mr Chambers as the most exact hitherto invented. "Let ABCD (No. 9.) represent a bucket of water, in which is the barometer eresom, which consists of a body ersm, and a tube ezys: the body and tube are both concave cylinders communicating with one another, and made of tin: the bottom of the tube zys has a lead weight to sink it so that the top of the body may just swim even with the surface of the water by the addition of some grain weights on the top. The water, when the instrument is forced with its mouth downwards, gets up into the tube to the height yu. There is added on the top a small concave cylinder, which I call the pipe to distinguish it from the bottom small cylinder which I call the tube. This pipe is to sustain the instrument from sinking to the bottom: md is a wire; mrs, des, are two threads oblique to the surface of the water, which threads perform the office of diagonals: for that while the instrument sinks more or less by the attraction of the gravity of the air, there where the surface of the water cuts the thread, is formed a small bubble; which bubble ascends up the thread, as the mercury in the common barometer ascends."

The dimensions of this instrument given there are, 21 inches for the circumference of the body, the altitude 4, each base having a convexity of 6½ inches. The inner circumference of the tube is 5¼ inches, and its length 4½; so that the whole body and tube will contain almost 2½ quarts. The circumference of the pipe, that the machine may not go to the bottom on every small alteration of the gravity of the air, is 2¼ inches; according to which dimensions, he calculates that it will require 44 grains to sink the body to the bottom, allowing it only four inches to descend; at the same time that it is evident, that the fewer grains that are required to sink it to this depth, the more nice the barometer will be. He also calculates, that when the mercury in the common barometer is 30½ inches high, the body with a weight of 44 grains on its top will be kept in equilibrium with the water; but when the mercury stands at 28 inches, only 19 grains can be supported; and lastly, by computing the lengths of the diagonal threads, &c. he finds, that his instrument is 1200 times more exact than the common barometer. The following are his observations on the use of it.

1. While the mercury of the common barometer is often known to be stationary 24 hours together, the bubble of the new barometer is rarely found to stand still one minute.

2. Suppose the air's gravity increasing, and accordingly the bubble ascending; during the time that it ascends 20 inches, it will have many short descents of the quantity of half an inch, one, two, three, or more inches; each of which being over, it will ascend again. These retrocessions are frequent, and of all varieties in quantity and duration, so that there is no judging of the general course of the bubble by a single inspection, though you see it moving, but by waiting a little time.

3. A small blast of wind will make the bubble descend; a blast that cannot be heard in a chamber of the town will sensibly force the bubble downward. The blasts of wind sensible abroad, cause many of the above-mentioned retrocessions, or accelerations in the general course; as I found by carrying my barometer to a place where the wind was perceptible.

4. Clouds make the bubble descend. A small cloud approaching the zenith, works more than a great cloud near the horizon. In cloudy weather, the bubble defending, a break of the clouds (or clear place) approaching to the zenith, has made the bubble to ascend; and after that break had passed the zenith a considerable space, the bubble again defended.

5. All clouds (except one) hitherto by me observed, have made the bubble to descend. But the other day, the wind being north, and the course of the bubble defending, I saw to the windward a large thick cloud near the horizon, and the bubble still defended; but as the cloud drew near the zenith, it turned the way of the bubble, making it to ascend; and the bubble continued ascending till the cloud was all past, after which it resumed its former descent. It was a cloud that yielded a cold shower of small hail.

These are the most remarkable contrivances for the improvement of the common barometer; and indeed we must agree with Mr. Chambers, that the last, on account of its being so exceedingly sensible, and likewise easy of construction, and portable, seems to deserve attention much more than the others, which are always the more unexact, and the less easily moved, according to the enlargement of their scale; whereas this is seemingly subject to no such inconvenience. It is evident, however, that none of these could be used at sea, on account of the unsteady motion of the ship; for which reason Dr. Hook thought of constructing a barometer upon other principles.

His contrivance was no other than two thermometers. The one was the common spirit-of-wine thermometer, which is affected only by the warmth of the air; the other, which acts by the expansion of a bubble of air included, is affected not only by the external warmth, but by the various weight of the atmosphere. Therefore, keeping the spirit thermometer as a standard, the excess of the ascent or descent of the other above it would point out the increase or decrease of the specific gravity of the atmosphere. This instrument is recommended by Dr. Halley, who speaks of it as follows. "It has been observed by some, that, in long keeping this instrument, the air included either finds a means to escape, or deposits some vapours mixed with it, or else for some other cause becomes less elastic, whereby in process of time it gives the height of the mercury somewhat greater than it ought; but this, if it should happen in some of them, hinders not the usefulness thereof, for that it may at any time very easily be corrected by experiment, and the rising and falling thereof are the things chiefly remarkable in it, the just height being barely a curiosity."

"I had one of these barometers with me in my late southern voyage, and it never failed to prognosticate and give early notice of all the bad weather we had, so that I depended thereon, and made provision accordingly; and from my own experience I conclude, that a more useful contrivance hath not for this long time been offered for the benefit of navigation."

A new kind of marine barometer hath lately been invented by Mr. Nairne. It differs from the common one in having the bore of the tube small for about two feet in its lower part; but above that height it is enlarged to the common size. Through the small part of the instrument, the mercury is prevented from ascending too hastily by the motion of the ship; and the motion of the mercury in the upper wide part is consequently lessened. Much is found to depend on the proper suspension of this instrument; and Mr. Nairne has since found, by experiment, the point from which it may be suspended so as not to be affected by the motion of the ship.

We must now speak of the barometer in its second character, namely, as an instrument for measuring accessible altitudes. This method was first proposed by M. Pascal; and succeeding philosophers have been at no small pains to ascertain the proportion between the sinking of the mercury, and the height to which it is carried. For this purpose, however, a new improvement in the barometer became necessary, viz. the making of it easily portable from one place to another, without danger of its being broken by the motion of the mercury in the tube. The common portable barometer is constructed as follows.

The tube containing the mercury, instead of having its lower end immersed in a vessel of that fluid, has it bound up in a leather bag not quite full of mercury; and though the external air cannot get into the bag to suspend the mercury in the tube by pressing on its surface as in the common one; yet it has the same effect, by pressing on the outside of the bag; which being pliant, yields to the pressure, and keeps the mercury suspended in the tube at its proper height. This bag is generally inclosed in a little box, through the bottom of which passes a screw; with this screw the bag may be compressed so as to force the mercury up to the top of the tube; which keeps it steady, and hinders it from breaking the tube by dashing against the top when it is carried about, which it is otherwise apt to do.

Among the number of portable barometers we may perhaps mention... perhaps reckon what Mr. Boyle called his Statical barometer. It consisted of a glass bubble, about the size of a large orange, and blown very thin, so as to weigh only 70 grains. This being counterpoised by brass weights in a pair of scales that would turn with the thirtieth part of a grain, was found to act as a barometer. The reason of this was, that the surface of the bubble was opposed to a vastly larger portion of air than that of the brass weight; and consequently behaved to be affected by the various specific gravity of the atmosphere: thus when the air became specifically light, the bubble defended, and vice versa; and thus, he says, he could have perceived variations of the atmosphere no greater than would have been sufficient to raise or lower the mercury in the common barometer an eighth part of an inch.

The portable barometer, as already observed, has long been in use for the mensuration of accessible altitudes; and, in small heights, was found to be more exact than a trigonometrical calculation, the mercury descending at the rate of about one inch for 800 feet of height to which it was carried: but, in great heights, the most unaccountable differences were found between the calculations of the most accurate observers; so that the same mountain would sometimes have been made thousands of feet higher by one person than another; nay, by the same person at different times. All these anomalies M. de Luc of Geneva undertook to account for, and to remove; and in this undertaking he persisted with incredible patience for 20 years. The result of his labour is as follows.

The first cause of irregularity observed was a fault in the barometer itself. M. de Luc found, that two barometers, though perfectly alike in their appearance, did not correspond in their action. This was owing to air contained in the tube. The air was expelled by boiling the mercury in them; after which, the motions of both became perfectly consonant. That the tubes may bear boiling, they must not be very thick, the thickness of the glass not above half a line; and the diameter of the bore ought to be from two and an half to three lines. The operation is performed in the following manner: A chafing dish with burning coals is placed on a table; the tube, hermetically sealed at one end, is inverted and filled with mercury within two inches of the top; the tube is gradually brought near the fire, moving it obliquely up and down, that the whole length of it may be heated; and advancing it nearer and nearer, till it is actually in the flame, the globules of air begin to move visibly towards the top. The boiling at last commences; and it is easy to make it take place from one end to the other, by causing the several parts of the tube successively pass with rapidity through the flame.

The next cause of variation, was a difference of temperature. To discover the effects of heat on the mercury, several barometers were chosen that for a long time had been perfectly consonant in their motions. One of these was placed in an apartment by itself, to mark the change in the external air, if any should happen. The rest were situated in another apartment, along with three thermometers, graduated according to the scale of M. De Reamur, and exactly correspondent with one another. The point at which the mercury stood when the experiment began, was carefully noted, and also the precise height of the thermometers. The latter apartment then was gradually heated; and with so much uniformity, that the thermometers continued still to agree. When the heat had been augmented as much as possible, the altitudes both of the barometers and thermometers were again accurately marked, to ascertain the differences that corresponded to one another. This experiment was repeated several times with next to no variation; and from the barometer in the first apartment it appeared, that no sensible alteration had taken place in the external air. Hence M. De Luc found, that an increase of heat sufficient to raise the thermometer from the point of melting ice to that of boiling water, augments the height of the mercury in the barometer precisely six lines; and therefore, dividing the distance between these two points on the thermometer into 96 equal parts, there will be 1/96th of a line to add to, or subtract from, the height of the mercury in the barometer, for every degree of variation of the thermometer so graduated. A scale of this kind, continued above boiling or below freezing water, accompanies his portable barometer and thermometer.—So accurate, he says, did long practice make him in barometrical observations, that he could distinguish a variation of 1/96 of a line in the height of the mercury. He allows of no inclination of the tube, or other means to augment the scale, as all these methods diminish the accuracy of the instrument. Two observations are always required to measure the altitude of a mountain: one with a barometer left on the plain, and another on the summit; and both must be accompanied with a thermometer.

His portable barometer consists of two tubes, one M. De Luc's portable barometer of 34 French inches in length; and from the top, for this length, perfectly straight; but, below this, it is bent round, so that the lower end turns up for a short space, parallel to the straight part. On this open end is fixed a cock; and on the upper side of this cock, is placed another tube, of the same diameter with the former, eight inches in length, open at both ends, and communicating with the long tube, through the cock. When the barometer is carried from one place to another, it is inverted very slowly, to hinder any air getting in; the quicksilver retires into the long tube on which the key of the cock is turned; and to prevent the cock from too great pressure of the mercury, the barometer is conveyed about in this inverted posture. When an observation is to be made, the cock is first opened; the tube is then turned upright, very slowly, to prevent, as much as possible, all vibration of the mercury, which disturbs the observation; and, according to the weight of the atmosphere, the mercury falls in the longer branch, and rises up through the cock, into the shorter.

The whole of the cock is made of ivory, except the key. The extremities of the tubes are wrapped round with the membrane employed by the gold-beaters, done over with fish-glue, in order to fix them tight, the one in the lower, and the other in the upper, end of the perpendicular canal of the cock. The part of the key that moves within the cock is of cork, and the outward part or the handle is of ivory. The cork is fastened firmly to the ivory by means of a broad thin plate of steel, which cuts both the ivory and cork, length-wise, through the centre, and reaches inward. to the hole of the key. This plate also counteracts the flexibility of the cork, and makes it obey the motion of the handle, notwithstanding it is very considerably compressed by the ivory, to render it tight. That this compression may not abridge the diameter of the hole of the key, it is lined with a thin hollow ivory cylinder, of the same diameter with the tubes.

On the upper end of the shorter tube is fixed, in the intervals of observation, a kind of funnel, with a small hole in it, which is fitted with an ivory stopple. The use of it is to keep the tube clean, to replace the mercury that may have made its way thro' the cock in consequence of any dilatation, and likewise to replace the mercury taken out of the shorter tube, after shutting the cock, on finishing an observation; because, when the mercury is left exposed to the air, it contracts a dark pellicle on its surface, that fulfils both itself and the tube. The shorter tube should be wiped from time to time, by a little brush of sponge fixed on the end of a wire.

The barometer, thus constructed, is placed in a long box of fir, the two ends of which are lined on the inside with cushions of cotton, covered with leather. This box may be carried on a man's back, like a quiver, either walking or riding; and should have a cover of wax-cloth, to defend it against rain. It should be kept at some distance from the body of the man, and be protected from the sun by an umbrella, when near the place of observation, to prevent its being affected by any undue degree of heat. The barometer should, further, be attended with a plummet, to determine the perpendicular position of it; and a tripod, to support it firm in that position at the time of observation.

The scale of the barometer begins on the long tube, at a point on a level with the upper end of the short one; and rises, in the natural order of the numbers, to 21 inches. Below the above point, the scale is transferred to the short tube; and depends on it, in the natural order of the numbers, to 7 inches. The whole length of the scale is 28 French inches; and since, as the mercury falls in the one tube, it must rise in the other; the total altitude will always be found by adding that part of the scale, which the mercury occupies in the long tube, to that part of it which the mercury does not occupy in the short one. In estimating, however, the total fall or rise on the long tube, every space must be reckoned twice; because, of barometers of this construction, half the real variation only appears in one of the branches.

Near the middle of the greater tube, is placed the thermometer abovementioned, for ascertaining the corrections to be made on the altitude of the mercury, in consequence of any change in the temperature of the air. It is placed about the middle of the barometer, that it may partake as much as possible of its mean heat. The ball is nearly of the same diameter with the tube of the barometer, that the dilatations or condensations of the fluids they contain may more exactly correspond. The scale is divided into 96 parts; between the points of boiling water and melting ice, and the term of 0, is placed one eighth part of this interval above the lower point; so that there are 12 degrees below, and 84 above, it. The reason for placing 0 here is, that, as 27 French inches are about the mean height of the barometer, so the 12th degree above freezing is nearly the mean altitude of the thermometer. Hence, by taking these two points, the one for the mean altitude, and the other for the mean heat, there will be fewer corrections necessary to reduce all observations to the same state, than if any higher or lower points had been fixed upon.

If then the barometer remain at 27 inches, and the thermometer at 0, there are no corrections whatever to be made. But if, while the barometer continues at 27 inches, the thermometer shall rise any number of degrees above 0, so many sixteenths of a line must be subtracted from the 27 inches, to obtain the true height of the barometer, produced by the weight of the atmosphere, and to reduce this observation to the state of the common temperature. If, on the other hand, the thermometer shall fall any number of degrees below 0, while the barometer still stands at 27 inches, so many sixteenths must be added to that height, to obtain the true altitude.

Nothing is more simple than these corrections, when the barometer is at or near 27 inches of height. If, however, it fall several inches below this point, as the portable barometer very frequently must, the dilatations will no longer keep pace with the degrees of heat, after the rate of $\frac{1}{16}$ of a line for every degree of the thermometer; because, the columns of mercury being shortened, the quantity of fluid to be dilated will be diminished. The truth is, the quantity of the dilatations for the same degree of heat is just as much diminished as the column is shortened. If, then, it shall still be found convenient to reckon the dilatations by sixteenths of a line, these sixteenths must be counted on a scale, of which the degrees shall be as much longer than the degrees of the first scale, as the shortened column of mercury is less than 27 inches, the height to which the length of the degrees of the first scale was adapted. For instance, let the mercury descend to 13$\frac{1}{2}$ inches, half the mean column, and let the thermometer ascend 10 degrees above the mean heat; 10 sixteenths should be deducted from the mean column, for this temperature, according to the rule; but 10 half-sixteenths only, or 5 whole sixteenths, must be subtracted from the column of 13$\frac{1}{2}$ inches, because the sum of its dilatations will be half that of the former, the quantities of fluid being to one another in that proportion.

It would cause considerable embarrassment if the sixteenths of correction were always to be subdivided into less fractions, proportional to every half inch of descent of the barometer; and the same end is obtained in a very easy manner, by reckoning the corrections on different scales of the same length, but of which the degrees are longer according as the columns of the barometer are shorter. For example, the degrees of correction on the scale applicable to the column of 13$\frac{1}{2}$ inches, will be double in length what the same degrees are for the column of 27 inches; and, of course, the number of corrections will be reduced likewise one half, which we have seen by the rule they ought to be.

The author constructed, on a piece of vellum, scales with these properties, for no less than 23 columns of mercury, being all those between 18 inches and 29 inclusive, counting from half inch to half inch; within which extremes, every practical case will be comprehended. He wrapped this vellum on a small hollow cylinder, including a spring, like a spring-curtain, and fixed. fixed it on the right side of the thermometer. The vellum is made to pass from right to left, behind the tube of the thermometer, and to graze along its surface. The observer, to find the corrections to be made, pulls out the vellum till the scale corresponding to the observed altitude of the barometer comes to touch the thermometer, and on that scale he counts them. The vellum is then let go, and the screw gently furls it up.

The author having now, as he imagined, completely finished the instruments necessary for the accurate mensuration of heights; proceeded to establish, by experiment, the altitudes corresponding to the different defects of the mercury. Much had been written, and many rules had been given, on this subject, by different eminent philosophers, since the days of Pascal, who first broached it: but these disagreed so much with one another, and presented so little good reason why any one of them should be preferred, that no conclusion could, with confidence, be deduced from them. It became requisite, therefore, to lay them all aside, and to endeavour to discover, by practice, what could not be ascertained by theory. Saleve, a mountain near Geneva, was chosen for the scene of these operations. This mountain is near 3000 French feet high. The height of it was twice measured by levelling, and the results of the mensurations differed only 10½ inches; though there intervened six months between them, and the total altitude was so considerable. On this mountain were chosen no less than 15 different stations, rising after the rate of 200 feet, one above another, as nearly as the ground would admit. At these stations, it was proposed to make such a number of observations as might be a good foundation, either for establishing a new rule of proportion between the heights of places and the defects of the mercury, or for preferring some one of those formerly discovered.

Little progress was made in this plan, when a phenomenon, altogether unexpected, presented itself. The barometer being observed, at one of the stations, twice in one day, was found to stand higher in the latter observation than in the former. This alteration gave little surprize, because it was naturally imputed to a change of the weight of the atmosphere, which would affect the barometer on the plain in the same manner. But it produced a degree of astonishment, when, on examining the state of the latter, it was found, instead of corresponding with the motions of the former, to have held an opposite course, and to have fallen while the other rose. This difference could not proceed from any inaccuracy in the observations, which had been taken with all imaginable care; and it was so considerable as to destroy all hopes of success, should the cause not be detected and compensated.

The experiment was repeated several times, at intervals, that no material circumstance might escape notice. An observer on the mountain, and another on the plain, took their respective stations at the rising of the sun, and continued to mark an observation, every quarter of an hour, till it set. It was found, that the lower barometer gradually descended for the first three quarters of the day, after which it re-ascented, till, in the evening, it stood at nearly the same height as in the morning; that the higher barometer ascended for the first three quarters of the day, and then descended, so as to regain likewise, about sunset, the altitude of the morning.

The following theory seems to account in a satisfactory manner for this phenomenon. When the sun rises above the horizon of any place, his beams penetrate the whole of the section of the atmosphere of which that horizon is the base. They fall, however, very obliquely on the greater part of it, communicate little heat to it, and consequently produce little dilatation of its air. As the sun advances, the rays become more direct, and the heat and rarefaction of course increase. But the greatest heat of the day is not felt even when the rays are most direct, and the sun is in the meridian. It increases while the place receives more rays than it loses, which it will do for a considerable time after mid-day; in like manner, as the tide attains not its highest altitude till the moon has advanced a considerable way to the west of the meridian. The heat of the atmosphere is greatest at the surface of the earth, and seems not to ascend to any great distance above it. The dilatations, for this reason, of the air, produced by the sun, will be found chiefly, if not solely, near the earth. A motion must take place, in all directions, of the adjacent air, to allow the heated air to expand itself. The heated columns extending themselves vertically, will become longer, and at the same time specifically lighter, in consequence of the rarefaction of their inferior parts. The motion of air, till it rises into wind, is not rapid; these lengthened columns, therefore, will take some time to diffuse their summits among the adjacent less rarefied columns that are not so high; at least, they will not do this as fast as their length is increased by the rarefaction of their bases.

The reader, we presume, anticipates the application of this theory to the solution of the phenomenon in question. The barometer on the plain begins to fall a little after morning, because the column of air that supports it becomes specifically lighter on account of the rarefaction arising from the heat of the sun. It continues to fall for the first three quarters of the day; because, during that time, the heat, and consequently the rarefaction, are gradually increasing. It rises again, after this period; because the cold, and of course the condensation, coming on, the specific gravity is augmented by the rushing in of the adjacent air. The equilibrium is restored, and the mercury returns to the altitude of the morning.

The barometer on the eminence rises after morning, and continues to do so for three fourths of the day, for two reasons. The density of the columns of air is greatest near the earth, and decreases as the distance from it increases. The higher, for this reason, we ascend in the atmosphere, we meet with air specifically lighter. But by the rarefaction of the base of the column that supports the mercury of the barometer on the eminence, the denser parts of that column are raised higher than naturally they would be if left to the operation of their own gravity. On this account, the higher barometer is pressed with a weight, nearly as great as it would sustain, were it brought down, in the atmosphere, to the natural place of that denser air now raised above it by the prolongation of the base of the column. The other reason is, that as the rarefaction does not take place at any great distance from the earth, little change is produced in the specific gravity of of the portion of the column that presses on the higher barometer, and the summit of that column dissipates itself more slowly than it increases. Thus, we see how this barometer must ascend during the first three fourths of the day, and pursue a course the reverse of that on the plain. The condensations returning after this time, the denser air subdues, the equilibrium takes place, and the mercury descends to its first position.

This phenomenon prompted the idea of a second pair of thermometers, to measure the mean heat of the column of air intercepted between the barometers. These thermometers are extremely delicate and sensible. The tubes are the finest capillary, the glass very thin, and the diameters of the balls only three lines. The balls are insulated, or detached from the scales, which are fixed to the tubes only by ligatures of fine brass-wire covered with silk. The air, by this contrivance, has free communication with the balls on all sides; and, if the direct rays of the sun be intercepted at some distance by a bit of paper, or even the leaf of a tree, the thermometers will quickly mark the true temperature of the air.

The reader, perhaps, will ask here, Could not this end have been gained by the first pair of thermometers? But we must request him to suspend his judgment, till we have explained the theory of computing the altitudes from the defects of the mercury. He will then find the scales of these thermometers so different, that neither of them could, without much inconvenience, serve the purpose of the other.

The altitudes are computed by logarithms. A table of logarithms contains two series of numbers, running parallel to one another. The first has its terms in geometrical progression, and the second its terms in arithmetical. The natural numbers $1, 2, 3, 4, \ldots$ form the first series; which, though in arithmetical progression when standing detached, are in geometrical regard of the second series; whose terms are in arithmetical progression, and are called logarithms, because they express the distance of their correspondent terms of the geometrical progression from the beginning of the series.

To apply this table to the present purpose: let us suppose the whole atmosphere divided into concentric spherical sections, whose common centre is that of the earth. Suppose, also, all these sections of equal thickness, namely, 12.497 toises, which is found to be the thickness of the lowest section, and balances a line of mercury, when the barometer stands at 348 lines or 29 inches. Add, then, all these sections together; and we shall have the total altitude of the atmosphere expressed in an arithmetical progression, whose common difference is 12.497 toises. Consequently, in this view, the heights are proportional to the logarithms.

It remains only to find the defects of the mercury, which measures the weights of the respective sections, in geometrical proportion, in order to justify the application of the logarithmic table to the computation of the altitudes. Now, it is easy to prove, in a very satisfactory manner, that the mean densities of these sections, which are in proportion of their weights, must be in geometrical progression, when the altitudes are in arithmetical; consequently, it is with great propriety and convenience that the logarithms are employed in the computation of the altitudes corresponding to the defects of the mercury. For, to find the vertical distance between two barometers, at different heights, no more is necessary than to look, in a table of logarithms, for the numbers that express in lines, or sixteenths of a line, the altitudes of the two columns of mercury, and take the logarithms of these numbers, whose difference will give this distance accurately, in thousandth parts of a toise. Multiply the toises by 6, which will furnish the altitudes in French feet.

The author made about 500 different observations at the several stations on the mountain of Saleve, which both suggested and verified the computation by logarithms. Many, however, of these observations, produced conclusions that deviated considerably from the results of the actual measurement, on account of the different temperatures in which they were taken. It was the design of the second pair of thermometers to point out the corrections of these deviations. In settling the scales necessary for this end, the first object was, to mark the temperature of all the observations where the logarithms gave the altitudes exactly, or nearly equal to what they were found to be by levelling. This temperature corresponded to 163° on the scale of Reaumur, and to 70° on that of Fahrenheit, and at it was fixed the term o. The next step was, to determine the corrections of the heights that became necessary, according as the state of the air was warmer or colder than the fixed point. With this view, all the remaining observations were collected, and compared with the different temperatures in which they were taken; and from an attentive examination of these circumstances, it was discovered, that for every 215 feet of height furnished by the logarithms, one foot of correction must be added or subtracted, for every degree of the thermometer, according as it stood above or below the term o.

The scale of Reaumur did not conveniently express this correction of 1 to 215. The author wished to adopt the ratio of 1 to 1000, in forming a new scale for that purpose; but the divisions would have been too small. He employed, therefore, that of 1 to 500; because, by doubling the degrees of the higher thermometer above or below o; or, which amounted nearly to the same thing, by doubling the mean heat of the column of air in taking the sum of the degrees of both thermometers, there resulted the ratio of 1 to 1000. The new scale, then, was divided by the following proportion: As 215, the last term of the ratio found by Reaumur's scale, is to 500, the last term of the ratio to be applied on the new scale; fo is 80, the parts between the fixed points of the first scale, to 186, the number of parts between the same points on the second. And as 80 is to 186, fo is 16½, the point on Reaumur's scale at which the logarithms give the altitudes without correction, to 39, the point at which they give them on the new scale. The term o is placed at this point, 39, at melting ice, and 147 at that of boiling water. To reduce all observations to the same temperature by this scale, nothing more is necessary than to multiply the heights found from the logarithms, by the sum of the degrees of both thermometers above or below o, and to divide the product by 1000. The quotient must be added to, or subtracted from, the logarithmic height, according as the temperature is positive or negative. As a specimen of the author's method, we shall now present our readers with the result of his operations at the 15 stations on Saleve. In one column are marked the heights found by levelling, and opposite to them the same heights found by the barometer; to the latter are prefixed the number of observations of which they are the mean.

| Stations | Heights by levelling | Number of observations | Heights by barometer | |----------|----------------------|-----------------------|----------------------| | | feet. inches | feet. | | 1 | 216 | 12 | 230½ | | 2 | 428 | 13 | 435½ | | 3 | 586 | 13 | 591½ | | 4 | 728 | 21 | 732½ | | 5 | 917 | 24 | 919½ | | 6 | 1218 | 27 | 1221½ | | 7 | 1420 | 23 | 1418½ | | 8 | 1800 | 17 | 1798½ | | 9 | 1965 | 17 | 1962½ | | 10 | 2211 | 17 | 2210 | | 11 | 2333 | 17 | 2331½ | | 12 | 2582 | 16 | 2583½ | | 13 | 2700 | 15 | 2703½ | | 14 | 2742 | 10 | 2741½ | | 15 | 2926 | 11 | 2924½ |

From this table, we presume the reader will be inclined to entertain the most favourable opinion of the abilities and industry of the author; but his barometer is probably susceptible of improvement. It seems too bulky and complex, and liable to accidents, and will require long practice to render other observers equally accurate and dextrous with him in its use. We hear, however, that the ingenious Mr Ramden of London, optician, has actually invented and constructed a portable barometer, as simple and light, almost, as the common stationary one. It is little apt to be disarranged by motion; and is capable, by the help of a Nonius index, to mark distinctly a variation of the mercury to the thousandth part of an inch, which corresponds, on the surface of the earth, to nearly 6 inches of height.