throughout. It is commonly much colder aloft; this ftate it may contain a confiderable portion of it is alfo of different conftitutions. Below it is other metals, particularly of fivér, bifmuth, and warm, loaded with vapour, and very expanfible; tin, which will diminish-its ipecific gravity. It has above it is cold, much drier, and less expanfible, been obtained by revivification from cinnabar of ath by its drynefs and its rarity. The currents the fpecific gravity 14229, and it is thought very of wind are often difpofed in ftrata, which long, fine ff 1365. Sir George Shuckburgh found the retain their places; and as they come from diffe- quickfiver which agreed precifely with the atmof.. reat regions, are of different temperatures and pherical obfervations on which the rules are founddifierent constitutions. We cannot therefore de- ́ed, to have the ipecific gravity 13°61. It is seldom termine the expanfion of the whole ftratum with, obtained fo heavy. It is evident that these variaprecision, and must be contented with an approxi- tions will change the whore refults; and that it is ration. The beft approximation that we can abfolutely neceflary, to obtain preciñon, that we make, is, by fuppofing the whole ftratum of a know the denfity of the mercury employed. The an temperature between thofe of its upper and fubtangent of the atmospherical logarithmic, or ower extremity, and employing the expanfion cor. the height of the homogeneous atmosphere, will responding to that mean temperature. This increase in the fame proportion with the denfity however, is founded on a gratuitous fuppofition of the mercury; and the elevation correfp nuing that the whole intermediate ftratum expands to one tenth of an inch of barometric height will alke, and that the expanfion is equable in the dif- change in the fame proportion. We mat. se conrest intermediate temperatures; but neither of tented with the remaining imperfections. For ang thefe are warranted by experiment. Rare air ex- purpose that can be anfwered by fuch meiurepands lefs than what is denfer; and therefore the ments of great heights, the method is fufliciently peteral expanfion of the whole ftratum, renders exact; but it is quite inadequate to the purpose density more uniform. Dr Horfley has point of taking accurate levels, Tr directing the coned out fome curious confequences of this in Phil. ftruction of canals, aqueducts, and other works of Tranf. Vol. LXIV. There is a particular eleva- this kind, where extreme precifion is abfolutely ta, at which the general expansion, instead of neceflary. diminishing the density of the air, increafes it by the iuperior expanfion of what is below; and we know that the expanfion is not equable in the in-, firmediate temperatures: but we cannot find out arde which will give us a more accurate correcton, than by taking the expansion for the mean perature.

We hall only add a few EASY RULES for the practice of this mode of measurement.

I. M. DE LUC'S METHOD.

I. Subtract the logarithm of the barometrical height at the upper station from the logarithm of that at the lower, and count the index and four first decimal figures of the remainder as fathỏms, the reit as a decimal fraction. Call this the elevation.

II. Note the different temperatures of the mercury at the two flations, and the mean temperature. Multiply the logarithmic expanfion corref ponding to this mean temperature (in Table B.) by the difference of the two temperatures, and fubtract the product from the elevation if the barometer has been coldeft at the upper ftation, otherwife add it. Call the difference or the fum the approximated elevation.

III. Note the difference of the temperatures of the air at the two stations by a detached thermometer, and alfo the mean temperature and i s difference from 32°. Multiply this difference by the expansion of air for the mean temperature, and multiply the approximate elevation by this product, according as the air is above or below 32°. The product is the correct elevation in fathoms and decimals.

When this is done, we have carried the method cf measuring heights by the barometer as far as it can go; and this fource of remaining error makes t needlefs to attend to fome other very minute equations which theory points out. Such is the Cominution of the weight of the mercury by the change of diftance from the centre of the earth. This accompanies the diminution of the weight of the air, but neither fo as to compenfate it, nor to go along with it pari paffu. After all, there 1a cafes where there is a regular deviation from 1 se rules, of which we cannot give any very faatory account. Thus, in the province of Qto a Peru, which is at a great elevation above Turface of the ocean, the heights obtained by De rules fall confiderably short of the real beats; and at Spitsbergen they confiderably ex them. It appears that the air in the circumpar regions, is denter than the air of the tempeer el mates when of the fine heat, and under tmc preffure; and the contrary feems to be the cafe with the air in the torrid zone. It would from that the specific gravity of air to mercury is * Spatbergen about ope to 19224, and in Peru out 1 to 13100. This difference is with great probability afcribed to the greater drynefs of the cumpolar air. This fource of error will always remain; and it al Hts. Temp. combined with another, which thould be atfeded to by all who practife this method of meafuing heights, namely, a difference in the specific anty of the quick-filver. It is thought fufficently pure for a barometer when it is cleared of a calcinable matter, fo as not to fully the tube. In

.

EXAMPLE. Suppofe that the mercury in the barometer at the lower ftation, was at 29'4 inches, that its temperature was 50°, and the temperature of the air was 45; and let the height of the mercury at the upper ftation be 25°19 inches, its te perature 46, and the temperature of the air 39.

Thus we have

29'4

25°19

50

464

I. Log. of 29'4
Log. of 25*19

Elevation in fathoms

Mean. Temp. Air. Mean.

B 2

671,191 II. Expanf.

throughout. It is commonly much colder aloft; it is alfo of different conftitutions. Below it is warm, loaded with vapour, and very expanfible; above it is cold, much drier, and less expanfible, both by its drynefs and its rarity,,, The currents of wind are often difpofed in ftrata, which long, retain their places; and as they come from different regions, are of different temperatures and different conftitutions. We cannot therefore determine the expansion of the whole ftratum with precition, and must be contented with an approxi- ́tions will change the whore results; and that it is mation. The beft approximation that we can make, is, by fuppofing the whole ftratum of a mean temperature between thofe of its upper and lower extremity, and employing the expanfion cor, reiponding to that mean temperature. This however, is founded on a gratuitous fuppofition that the whole intermediate ratum expands alike, and that the expansion is equable in the different intermediate temperatures; but neither of thefe are warranted by experiment. Rare air expands lefs than what is denfer; and therefore the general expanfion of the whole ftratum. renders its density more uniform. Dr Horfley has point ed out fome curious confequences of this in Phil. Tranf. Vol. LXIV. There is a particular elevation, at which the general expanfion, inftead of diminishing the density of the air, increafes it by the fuperior expanfion of what is below; and we know that the expanfion is not equable in the intermediate temperatures: but we cannot find out a rule which will give us a more accurate correction, than by taking the expansion for the mean temperature.

this ftate it may contain a confiderable portion of other metals, particularly of fiver, bifmuth, and tin, which will diminish its ipecific gravity. It has been obtained by revivification from cinnabar of 'the specific gravity 14°229, and it is thought very fine if 1365. Sir George Shuckburgh found the quickfilver which agreed precifely with the atmof pherical obfervations on which the rules are founded, to have the ipecific gravity 1361. It is feldom obtained fo heavy. It is evident that these variaabfolutely neceflary, to obtain preciñon, that we know the denfity of the mercury employed. The fubtangent of the atmospherical logarithmic, or the height of the homogeneous atmosphere, will increase in the fame proportion with the denfity of the mercury; and the elevation correfpinding to one tenth of an inch of barometric height will change in the fame proportion. We mutt se contented with the remaining imperfections. Foi any purpose that can be anfwered by fuch meatrements of great heights, the method is fufficiently exact; but it is quite inadequate to the purpofe of taking accurate levels, for directing the conftruction of canals, aqueducts, and other works of this kind, where extreme precifion is abfolutely neceflary.

When this is done, we have carried the method of measuring heights by the barometer as far as it can go; and this fource of remaining error makes it needlefs to attend to fome other very minute equations which theory points out. Such is the diminution of the weight of the mercury by the change of diftance from the centre of the earth. This accompanies the diminution of the weight of the air, but neither fo as to compenfate it, nor to go along with it pari paffu. After all, there are cafes where there is a regular deviation from thofe rules, of which we cannot give any very fatisfactory account. Thus, in the province of Quito in Peru, which is at a great elevation above the furface of the ocean, the heights obtained by the rules fall confiderably short of the real heights; and at Spitsbergen they confiderably ex ceed them. It appears that the air in the circumpolar regions, is denter than the air of the temperate climates when of the Inne heat, and under the fame preffure; and the contrary feems to be the cafe with the air in the torrid zone. It would feem that the fpecific gravity of air to mercury is Spitbergen about ope to 10224, and in Peru about 1 to 13100. This difference is with great probability afcribed to the greater drynefs of the crcumpolar air.

This fource of error will always remain; and it is combined with another, which fhould be attended to by all who practife this method of meainring heights, namely, a difference in the specific gravity of the quick-filver. It is thought fufficently pure for a barometer when it is cleared of all calcinable matter, so as not to fully the tube, In

We shall only add a few EASY RULES for the practice of this mode of measurement.

1. M. DE LUC'S METHOD.

I. Subtract the logarithm of the barometrical height at the upper station from the logarithm of that at the lower, and count the index and four first decimal figures of the remainder as fathoms, the reit as a decimal fraction. Call this the elevation.

II. Note the different temperatures of the mercury at the two flations, and the mean temperature. Multiply the logarithmic expanfion corref ponding to this mean temperature (in Table B.) by the difference of the two temperatures, and lubtract the product from the elevation if the barometer has been coldeft at the upper ftation, otherwife add it. Call the difference or the fum the approximated elevation.

III. Note the difference of the temperatures of the air at the two stations by a detached thermometer, and alfo the mean temperature and its differeuce from 32°. Multiply this difference by the expantion of air for the mean temperature, and multip.ythe approximate elevation by this product, according as the air is above or below 32°. The product is the correct elevation in fathoms and décimals.'

EXAMPLE. Suppofe that the mercury in the barometer at the lower ftation, was at 29'4 inches, that its temperature was 50°, and the temperature of the air was 45; and let the height of the mercury at the upper ftation be 25°19 inches, its tém perature 46, and the temperature of the air 39. Thus we have

Pic de los Reyes?

Pic du Medi

Pic d'Offano

Canegou

Like of Geneva

Mount Etna

Mount Veluvius

Pyrennees

Mount Hecla in Iceland
Snowdown

Benmore

Ben-Lawers

Ben-Gloe

Schiehallion

Ben Lomond
Tinto

Table Hill, Cape of Good Hope
Gondar city in Abyffinia

7620 to the common barometer for measurement of 9300 heights, on account of their bulk and cumber11700 fomenefs: nay, they are inferior for all philofo8544 phical purposes in point of accuracy. Their scale 1232 must be determined in all its parts by the com10954 mon barometer; and therefore notwithstanding 3938 their great range, they are fufceptible of no great4887 er accuracy, than that with which the fcale of a 3555 common barometer can be obferved and meafu3723 red. This is evident from confidering how the 3858 points of their fcale must be ascertained. The 3472 most accurate method for graduating fuch a ba 3461 rometer would be to make a mixture of vitriolic 3180 acid and water, which thould have one roth of 2342 the denfity of mercury. Then, let a long tube 3454 ftand verticle in this fluid, and connect its upper 8440 end with the open end of the barometer by a pipe 8082 which has a branch to which we can apply the 14026 mouth. Then if we fuck through this pipe, the 19595 Auid will rife both in the barometer and in the 19391 other tube; and 10 inches rife in this tube will 19290 correfpond to one inch defcent in the common 15670 barometer. In this manner may every point of 9977 the fcale be adjufted in due proportion to the 306 reft. But it still remains to determine what partiThis laft is fo fingular, that it is neceffary to cular point of the fcale correfponds to fonie degive the authority on which this determination is termined inch of the common barometer. This founded. It is deduced from nine years obferva- can only be done by an actual comparison; and Eous with the barometer at Astracan by Mr Lecre, this being done, the whole becomes equally accompared with a series of observations made with curate. Except therefore for the mere purpose the fame barometer at St Petersburgh. of chamber amusement, in which cafe the barometer laft described has a decided preference, the common barometer is to be preferred; and our attention should be entirely directed to its improvement and portability.

Source of the Nile

Pic of Teneriffe

Chimborazo

Cayabourow

Antifana

Fichincha

City of Quito

Caspian Sea below the ocean

This ufe of the barometer has rendered it a very interefting inftrument to the philofopher and to The traveller; and many attempts have been made o late to improve it, and render it more portable. The improvements have either been directed to the enlargement of its range, or to the more accurate measurement of its prefent fcale. Of the rft kind are Hooke's wheel barometer, the diacoral barometer, and the horizontal barometer. See BAROMETER, 4, 6; alfo § ro, 20; for two sary ingenious contrivances of Mr Rownings, which are not portable. Of all the barometers with an enlarged fcale the beft is that invented by Dr Hooke in 1668, and defcribed in the Phil. Tranh N 185. The invention was alfo claimed by Huygens and De la Hire; but Hooke's was publifhed long before.

It confifts of a compound tube ABCDEFG (fig. $1. Pl. 281.) of which the parts AB and DE are equally wide, and EFG as much narrower as we would amplify the scale. The parts AB and EG muft alfo be as perfectly cylindrical as poffible. The part HBCDI is filled with mercury, having a Vacuum above in AB. IF is filled with a light fluid, and FG with another light fluid which will not mix with that in IF. The ciftern G is of the Lame diameter as AB. The range of the feparat ing furface at F is as much greater than that of the farface 1, as the area of 1 is greater than that of F. And this ratio is in our choice. This barometer free from all the bad qualities of thofe formerly defcribed, being moft delicately moveable; and is by far the fitteft for a chamber, or amusement, by obfervations on the changes of the atmospheric preffure. The flighteft breeze caufes it to rife and fall, and it is continually in motion.

But this, and all other barometers are inferior

For this purpofe it should be furnished with two microscopes or magnifying glaffes, one ftationed at the beginning of the fcale; which fhould either be moveable, fo that it may always be brought to the furface of the mercury in the ciftern, or the ciftern fhould be fo contrived that its furface may, always be brought to the beginning of the fcale. The glafs will enable us to fee the coincidence with accuracy. The other microfcope must be moveable, fo as to be set oppofite to the furface of the mercury in the tube; and the scale should be furnished with a vernier which divides an inch into 1000 parts, and be made of materials of which we know the expansion with great precision.

For an account of many ingenious contrivances to make the inftrument accurate, portable, and commodious, confult Magellan, Differ. de diverfes Inftr. de Phys; Phil. Tranf. xvii. ixviii.; Journ. de Phys. xix. 108. 346. xvi. 392. xviii. 391..xxi. 436. xxii. 390.; Sulzer, A&t Helvet. iii. 259.; De Luc, Recherches fur les Modifications de l'Atmosphere, i. 401. ii. 459, 490. De Luc's feems the most fimple and perfect of them all. Cardinal de Luynes (Mem. Par. 1768); Prin. De Luc, Recherches, § 63.; Van Swinden's Pofitiones Phyfica; Com. Acad. Petrop...; Com. Acad. Petrop. Nov. 100. viii.

SECT. VIII. Of AIR in MOTION.

THUS We have given an elementary account of the diftinguishing properties of air as a heavy and compreflible fluid, and of the general phenomena which are immediate confequences of these pro

perties;

AIR is about 840 times lighter than water, and the preffure of the atmosphere fupports water at the height of 33 feet nearly. The height therefore of a homogeneous atmosphere is nearly 33 X 840, or 27720 feet. As for the velocity acquired by any fall, a heavy body by falling one foot acquires the velocity of 8 feet per fecond; and, the velocities acquired by falling thro' different heights are as the fquare roots of the heights. Therefore, to find the velocity correfponding to any height, expreffed in feet per fecond, multiply the fquare root of the height by 8. We have therefore in the prefent inftance V-8√27220,8 × 166,493

perties; in a fet of propofitions analagous to those which form the doctrines of HYDROSTATICS. We fhall now confider it as moveable and inert. The phenomena confequent on these properties are exhibited in the velocities which air acquires by preffure, in the refiftance which bodies meet with to their motion thro' the air, and in the impreffion which air in motion gives to bodies expofed to its action., We fhall first confider the motions of which air is fufceptible when the equilibrium of preffure (whether arising from its weight or its elafticity) is removed; and next, we fhall confider its action on folid bodies expofed to its current, and the refiftance which it makes to their motion through it. "In this confideration we fhall adapt our invef-1332 feet per fecond. This therefore is the tigation to the circumftances in which compref- velocity with which common air will rush into a fible fluids are most commonly found. We fhail void; and this may be taken as a ftandard numconfider air therefore as it is commonly found in ber in pneumatics, as 16 and 32 are standard numacceffible fituations, as acted on by equal and pabers in the general science of mechanics, expreffing rallel gravity; and we shall confider it in the fame order in which water is treated in a system of

HYDRAULICS.

In that science the leading problem is to deter. mine with what velocity the water will move through a given orifice when impelled by fome known preffure; and it has been found, that the beft form in which this moft difficult and intricate propofition can be put, is to determine the velo. city of water flowing through this orifice when impelled by its weight alone. Having determined this, we can reduce to this cafe every queftion which can be propofed; for, in place of the pref. fure of any pifton or other mover, we can always fubftitute a perpendicular column of water or air, whofe weight thall be equal to the given preffure, The first problem, therefore, is to determine with what velocity air will rush into a void when im pelled by its weight alone. This is evidently analogous to the hydraulic problem of water flowing

cut of a veffel.

And here we must refer our readers to the for Intions which have been given of that problem, under HYDROSTATICS, Part I. and the demonftration that it flows with the velocity which a heavy Fody would acquire by falling from a height equal to the depth of the hole under the furface of the water in the veffel. In whatever way we attempt to demonftrate that propofition, every fep, nay, every word, or the demonftration applies equally to the air, or to any fluid whatever. Or, if our

readers fhould wifh to fee the connection or ana

logy of the cafes, we only defire them to recollect an undoubted maxim in regard to motion, that when the moving force and the matter to be moved vary in the fame proportion, the velocity will be the fame. If therefore there be fimilar veffels of air, water, oil, or any other fluid, all of the height of a homogeneous atmosphere, they will all run through equal and fimilar holes with the fame velocity; for in whatever proportion the quantity of matter moving thro' the hole be varied by a variation of denfity, the preffure which forces it out, by acting in circumstances perfectly fimilar, varies in the fame proportion by the fame variation of denfity. We must therefore affume it as the leading propo fition, that air rufes from the atmosphere into a void with the velocity which a heavy body would acquire by falling from the top of a homogeneous atmosphere.

the action of gravity at the furface of the earth. Greater precifion is not neceffary in this matter. The height of a homogeneous atmosphere is a variable thing, depending on the temperature of the air. If this feems any objection against the ufe of the number 1332, we may retain 8/H in place of it, where H expreffes the height of a homogeneous atmosphere of the given temperature. A variation of the barometer makes to change in the velocity, nor in the height of the homogeneous atmosphere, because it is accompanied by a proPortional variation in the denfity of the air. When it is increated one 10th, for inftance, the denfity force and the matter to be moved are changed in is alfo increafed one roth; and thus the expelling the fame proportion, and the velocity remains the fame. We do not here confider the velocity which the air acquires after its iffuing into the void by its continual expansion. This may be afcertained by the 39th prop. of Newton's Principia, i. Nay, appears, very paradoxical, if a cylinder of air, communicating in this manner with a void, which pretics it down as the air flows out, and be compreffed by a piston loaded with a weight, thus keeps it of the fame denfity, the velocity of eflux with full be the fame, however great the pref fure may be for the firft and immediate effect of the load on the pitton is to reduce the air in the cylinder to fuch a denfity that its clafticity hall exactly balance the load; and because the elafticity of air is proportional to its denfity, the denfity of the air will be increafed in the fame proportion with the load, that is, with the expelling power; for we are neglecting at prefent the weight of the included air as too inconfiderable to have any fenfible effect. Therefore, fince the matter to be moved is increafed in the fame proportion with the preffure, the velocity will be the fame as before.

which

:

It is equally eafy to determine the velocity with which the air of the atmosphere will rush into a pace containing rarer air. Whatever may be the denfity of this air, its elafticity, which follows the proportion of its denfity, will balance a proportional part of the preffure of the atmosphere; and ving force. The matter to be moved is the fame it is the excefs of this laft only which is the moas before. Let D be the natural density of the air, and the denfity of the air contained in the veffel into which it is fuppofed to run, and let P be the

preflure