Chamber barometer by Mr W 1liam Jones. 2) vernier fcale. Fig. 10. reprefents a kind of Chamber Barometer, or a complete inftrument for observing in a fixed place, fuch as a room, &c. the changes in the atmosphere. It is constructed by Mr W. Jones optician, London; and confifts of barometer d, thermometer aa, and hygrometer c, all in one mahogany frame. One advantage of this inftrument is, that either the thermometer or hygrometer may be taken from the frame, and occafionally made ufe of in another place if required. The thermometer is feparated by only unfcrewing two fcrews a, a; and the hygrometer, by unscrewing a brass pin at the back of the frame, not feen in this figure. The index of the hygrometer is at any time fet, by only moving with your finger the brafs wheel feen at c; the two fliding indexes of the barometer and thermometer are moved by a rack-work motion, set in action by the key g placed in the holes h and i. The divifions of the barometer plate b are in tenths of an inch, from 28 to 31 inches; these again fubdivided into hundredths by means of the vernier fcale, placed oppofitely on a fliding flip of brass fimilar to the common barometers, moft of which are now made with this vernier. On this vernier are ten equal parts, or divifions; (fee A, fig. 11. which for the fake of perMethod of fpicuity is drawn larger). All of thefe together are equal ufing the juft to eleven of thofe on the fcale of inches; that is, to eleven tenths. By this artifice the height of the mercury at E is evident by infpection only, to the one -hundredth part of an inch. To understand this, nothing more is neceffary than to confider, that one tenth part of a tenth of an inch is the one hundredth part of an inch. Now every tenth of an inch in the fcale B is divided into ten equal parts by the flip or vernier A: for fince ten divifions on that exceed ten on the fcale by one divifion, that is, by one-tenth of an inch; there fore one divifion on the vernier will exceed one divifion on the scale by one-tenth part; and two divifions on the vernier will exceed two on the fcale by two tenths, and fo on: Therefore every divifion on the vernier will exceed the fame number of divifions on the fcale by fo many tenths of a tenth, or by fo many hundredth parts of an inch. Therefore the ten equal divifions of an inch on the scale B, muft be looked upon as fo many ten hundredth parts of an inch, and numbered thus, 10. 20. 30. 40, &c. parts of an inch; then the vernier gives the unit to each ten, thus: Set the index C very nicely to the top of the furface of the mercury E; and if at the fame time the beginning of the divifions at C coincide with a line of divifion in the scale B, then it shows the altitude of the mercury in inches and tenths of an inch exactly. But fuppofe the index line C of the vernier falls between two divifions or tenths on the fcale B, then there will be a coincidence of lines in both at that number of the vernier, which shows how many tenth parts of that tenth the index of the vernier has paffed the laft decimal divifion of the fcale. Thus, for example, suppose the index of the vernier were to point fomewhere between the fixth and feventh tenth above 30 on the fcale: then if, by looking down the vernier, you obferve the coincidence at number 8, it shows that the altitude of Barometer. the mercury is 30 inches and 68 parts of a hundredth of another inch; or fimply thus, 30.68 inches. The fcrew at fig. 1o. ferves to prefs the mercury quite up into the tube, when required to be much moved or carried about, thereby rendering the barometer of the kind called portable. To the lower extremity of the tube (fee fig. 14.) is cemented a wooden refervoir A, with a kind of leathern bag at bottom, the whole containing the mercury, but not quite full: and though the external air cannot get into the bag to fufpend the mercury in the tube, by preffing on its furface, as in the common one; yet it has the fame effect by preffing on the outfide of the bag; which being flexible, yields to the preffure, and keeps the mercury fufpended in the tube to its proper height. Through the under part of the frame paffes the fcrew f, with a flat round plate at its end; by turning of this fcrew, the bag may be fo compreffed as to force the mercury up to the top of the tube, which keeps it fteady, and hinders the tube from breaking by the mercury dafhing against the top when carried about, which it is otherwise apt to do. 30 Mr Nairne. A new kind of marine barometer hath lately been Marine ba invented by Mr Nairne. It differs from the common rometer by one in having the bore of the tube fmall for about two feet in its lower part; but above that height it is enlarged to the common fize. Through the fmall part of the inftrument the mercury is prevented from afcending too haftily by the motion of the fhip; and the motion of the mercury in the upper wide part is confequently leffened. Much is found to depend on the proper fufpenfion of this inftrument; and Mr Nairne has fince found, by experiment, the point from which it may be fufpended fo as not to be affected by the mo tion of the fhip. 31 Another marine barometer has been invented by one By Paffe Paffemente, a French artift. It is only a common one mente. having the middle of the tube twisted into a spiral confifting of two revolutions. By this contrivance, the impulfes which the mercury receives from the motions of the fhip are destroyed by being tranfmitted in contrary directions. 32 the menfu We must now speak of the barometer in its fecond Bar meter character, namely, as an inftrument for measuring ac- applied to ceffible altitudes. This method was firft propofed by the menf M. Pafcal; and fucceeding philofophers have been at altitudes. no fmall pains to ascertain the proportion between the finking of the mercury and the height to which it is carried. For this purpose, however, a new improvement in the barometer became neceffary, viz. the ma king of it eafily portable from one place to another, without danger of its being broken by the motion of the mercury in the tube; which was effected by the.. contrivance already mentioned. 33 Among the number of portable barometers we may Statical bas perhaps reckon what Mr Boyle called his Statical Barometer. rometer. It confifted of a glass bubble, about the fize of a large orange, and blown very thin, fo as to weigh only 70 grains. This being counterpoifed by brafs weights in a pair of fcales that would turn with the 30th part of a grain, was found to act as a barometer. The reafon of this was, that the furface of the bubble was opposed to a vaftly larger portion of air than that 34 Method of Barometer. of the brass weight, and confequently liable to be globules of air begin to move vifibly towards the top Barometer, affected by the various fpecific gravity of the atmo- The boiling at laft commences; and it is eafy to make fphere: thus, when the air became fpecifically light, it take place from one end to the other, by caufing the the bubble defcended, and vice verfa; and thus, he feveral parts of the tube fucceffively pafs with rapidity fays, he could have perceived variations of the atmo- through the flame. By this operation the mercury is sphere no greater than would have been fufficient to freed from all aerial particles, particularly thofe which raife or lower the mercury in the common barometer line the infide of the tube, and which cannot easily be an eighth part of an inch. got clear of by any other method. When this last stratum of air is difcharged, the tube may be afterwards emptied, and filled even with cold mercury, when it will be found nearly as free of air as before. cury in the tube thus prepared by a determinate quantity of heat, will rife higher than those in the common fort, and the barometers will more nearly correfpond with each other; whereas there will be a difference of fix or eight lines in the afcent of mercury in the common barometers. Inftruments of this kind rife uniformly in a heated room, whilft those of the common kind defcend in different proportions. On cooling the room, the former defcend uniformly, while the latter defcend unequally, by reafon of the unequal proportions of air in them. the changes To these we may add an account of a new and very measuring fingular barometer mentioned by M. Lazowski in his tour through Switzerland. "A Curè, fhortlighted, who nevertheless amufed himself with firing at a mark, thought of ftretching a wire in fuch a manner as to draw the mark to him, in order to fee how he had aimed. He obferved, that the wire fometimes founded as if it had been ofcillatory; and that this happened when a change was about to enfue in the atmofphere; fo that he came to predict with confiderable accuracy when there was to be rain or fine weather. On making further experiments, it was obferved, that this wire was more exact, and its founds more diftinct, when extended in the plane of the meridian than in other pofitions. The founds were more or less soft, and more or lefs continued, according to the changes of weather that were to follow; though the matter was not reduced to any accuracy, and probably is not capable of much. Fine weather, however, was faid to be announced by the founds of counter tenor, and rain by those of bass. M. Volta was faid to have mounted 15 chords at Pavia, in order to bring this method to fome perfection; but there are as yet no accounts of his fuccefs. 35 Difficulties in meafuring heights by the barometer. 36 Removed by M. De Luc. with the The portable barometer, as already obferved, has long been in ufe for the menfuration of acceffible altitudes; and, in small heights, was found to be more exact than a trigonometrical calculation, the mercury defcending 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 calculation of the most accurate observers; so that the fame mountain would sometimes have been made thousands of feet higher by one person than another; nay, by the fame perfon at different times. All these anomalies M. de Luc of Geneva undertook to account for, and to remove; and in this undertaking he perfitted with incredible patience for 20 years. The refult of his labour is as follows. The firft caufe of irregularity obferved was a fault in the barometer itfelf. M. de Luc found, that two barometers, though perfectly alike in their appearance, did not correfpond in their action. This was owing to air contained in the tube. The air was expelled by 37 boiling the mercury in them; after which, the motions Mercury of both became perfectly confonant. That the tubes how boiled may bear boiling, they must not be very thick, the in the tubes thickness of the glafs 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 fealed 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 effects. The mer heat. 38 The next caufe of variation was a difference of tem- Variation of perature. To difcover the effects of heat on the mer- the height cury, feveral barometers were chofen that for a long of the mer-time had been perfectly confonant in their motions. cry by One of these was placed in an apartment, by itself, to mark the change in the external air, if any fhould happen. The reft were fituated in another apartment, along with three thermometers, graduated according to the scale of M. de Reamur, and exactly correfpondent with one another. The point at which the mercury flood when the experiment began, was carefully noted, and alfo the precife height of the thermo meters. The latter apartment then was gradually heated; and with fo much uniformity, that the thermometers continued ftill to agree. When the heat had been augmented as much as poffible, the altitudes both. of the barometers and thermometers were again accurately marked, to afcertain the differences that correfponded to one another. This experiment was repeated feveral times with next to no variation; and from the barometer in the firft apartment it appeared, that no fenfible alteration had taken place in the external air. Hence M. de Luc found, that an increase of heat fufficient to raife the thermometer from the point of melting ice to that of boiling water, augments the height of the mercury in the barometer precifely fix lines; and therefore, dividing the distancebetween these two points on the thermometer into 96 equal parts, there will be th of a line to add to, or fubtract from, the height of the mercury in the barometer, for every degree of variation of the thermometer fo graduated. A scale of this kind, continued above boiling or below freezing water, accompanies his portable barometer and thermometer-So accurate, he fays, did long practice make him in barometrical obfervations, that he could diftinguish a variation of a line in the height of the mercury. He allows of no inclination of the tube, or other means to augment the fcale, as all these methods diminish the accuracy of the inftrument. Two obfervations are always required to measure the altitude of a mountain: one with a barometer left on the plain, and another on the fummit; and both must be accompanied with a thermometer. of Barometer. 39 M. De meter. 1 His portable barometer confifts of two tubes, one perpendicular pofition of it; and a tripod, to fupport Barometer. of 34 French inches in length; and from the top, for it firm in that pofition at the time of obfervation. this length, perfectly ftraight; but below this, it is The fcale of the barometer begins on the long tube, Lue's port- bent round, fo that the lower end turns ep for a short at a point on a level with the upper end of the short one; able baro fpace parallel to the ftraight part. On this open end and rifes, in the natural order of the numbers, to 21 is fixed a cock; and on the upper fide of this cock is inches. Below the above point, the scale is transferred placed another tube, of the fame diameter with the to the fhort tube; and defcends on it, in the natural former, eight inches in length, open at both ends, and order of the numbers, to 7 inches. The whole length communicating with the long tube, through the cock. of the fcale is 28 French inches; and fince, as the When the barometer is carried from one place to an- mercury falls in the one tube, it must rife in the other, other, it is inverted very flowly, to hinder any air get the total altitude will always be found by adding that ting in; the quickfilver retires into the long tube on part of the fcale, which the mercury occupies in the long which the key of the cock is turned; and to preferve tube, to that part of it which the mercury does not the cock from too great preffure of the mercury, the occupy in the short one. In eftimating, however, the barometer is conveyed about in this inverted pofture. total fall or rife on the long tube, every space muit be When an observation is to be made, the cock is first reckoned twice; becaufe, of barometers of this conopened; the tube is then turned upright, very flowly, ftruction, half the real variation only appears in one of to prevent, as much as poffible, all the vibration of the the branches. mercury, which disturbs the obfervation; and, according to the weight of the atmofphere, the mercury falls in the longer branch, and rifes 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 fifh-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 faftened firmly to the ivory by means of a broad thin plate of fteel, which cuts both the ivory and cork, lengthwife, 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 confiderably compressed by the ivory, to render it tight. That this compreffion may not abridge the diameter of the hole of the key, it is lined with a thin hollow ivory cylinder, of the fame diameter with the tubes. On the upper end of the fhorter tube is fixed, in the intervals of obfervation, a kind of funnel, with a small hole in it, which is fhut with an ivory ftopple. The ufe of it is to keep the tube clean; to replace the mercury that may have made its way through the cock in confequence of any dilatation; and likewife to replace the mercury taken out of the fhorter tube; after shutting the cock, on finishing an obfervation; because, when the mercury is left exposed to the air, it contracts a dark pellicle on its furface, that fullies both itfelf and the tube. The fhorter tube fhould be wiped from time to time, by a little bruth of sponge fixed on the end of a wire. The barometer, thus conftructed, is placed in a long box of fir, the two ends of which are lined on the infide 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 fhould have a cover of wax-cloth, to defend it againft rain. It should be kept at fome distance from the body of the man, and be protected from the fun by an umbrella, when pear the place of obfervation, to prevent its being affected by any undue degree of heat. The barometer fhorld, farther, be attended with a plummet, to determine the Near the middle of the greater tube is placed the thermometer abovementioned, for afcertaining the corrections to be made on the altitude of the mercury in confequence 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 poffible of its mean heat. The ball is nearly of the fame diameter with the tube of the barometer, that the dilatations or condenfations of the fluids they contain may more exactly correfpond. The fcale is divided into 96 parts; between the points of boiling water and melting ice, and the term of o is placed one eighth part of this interval above the lower point; fo that there are 12 degrees below, and 84 above, it. The reafon for placing o here is, that as 27 French inches are about the mean height of the barometer, fo the 12th degree above freezing is nearly the mean altitude of the thermometer. Hence, by taking these two points, the one for the mean alti tude, and the other for the mean heat, there will be fewer corrections neceffary to reduce all obfervations to the fame ftate, than if any higher or lower points had been fixed upon. If then the barometer remains at 27 inches, and the thermometer at o, there are no corrections whatever to be made. But if, while the barometer continues at 27 inches, the thermometer shall rife any number of degrees above o, fo many fixteenths of a line must be fubtracted from the 27 inches, to obtain the true height of the barometer produced by the weight of the atmosphere, and to reduce this obfervation to the state of the common temperature. If, on the other hand, the thermometer fhall fall any number of degrees below o, while the barometer ftill ftands at 27 inches, fo many fixteenths must be added to that height, to obtain the true altitude. Nothing is more fimple than these corrections, when the barometer is at or near 27 inches of height. If, however, it fall feveral inches below this point, as the portable barometer very frequently, muft, the dilata tions will no longer keep pace with the degrees of heat, after the rate of of a line for every degree of the thermometer; because the columns of mercury being fhortened, the quantity of fluid to be dilated will be diminithed. The truth is, the quantity of the dilata tions for the fame degree of heat is juft as much dimi nifhed as the column is fhortened. If, then, it fhall total altitude was fo confiderable. On this mountain Barometer. were chofen no less than 15 different ftations, rifing after the rate of 200 feet, one above another, as nearly as the ground would admit. At these stations, it was propofed to make fuch a number of observations as might be a good foundation either for etablishing a new rule of proportion between the heights of places and the defcents of the mercury, or for preferring fome one of those formerly discovered. Barometer. ftill be found convenient to reckon the dilatations by fixteenths of a line, these fixteenths must be counted on a fcale, of which the degrees fhall be as much longer than the degrees of the firft fcale, as the fhortened column of mercury is less than 27 inches, the height to which the length of the degrees of the first scale was adapted. For inflance, let the mercury defcend to 13 inches, half the mean column, and let the thermometer afcend 10 degrees above the mean heat; 10 fixteenths fhould be deduced from the mean column, for this temperature, according to the rule; but 10 halffixteenths only, or 5 whole fixteenths, must be fubtracted from the column of 13 inches, because the fum of its dilatations will be half that of the former, the quantities of fluid being to one another in that proportion. mountain of Saleve. It would caufe confiderable embarraffment if the fixteenths of correction were always to be fubdivided into lefs fractions, proportional to every half inch of descent of the barometer: and the fame end is obtained in a very eafy manner, by reckoning the corrections on different fcales of the fame 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 fcale applicable to the column of 13 inches, will be double in length what the fame degrees are for the column of 27 inches; and of course the number of corrections will be reduced likewife one half, which we have seen by the rule they ought to be. The author conftructed, on a piece of vellum, fcales with these properties, for no lefs than 23 columns of mercury, being all thofe between 18 inches and 29 inclufive, counting from half inch to half inch; within which extremes, every practical cafe will be comprehended. He wrapped this vellum on a fmall hollow cylinder, including a fpring, like a fpring-curtain, and fixed it on the right fide of the thermometer. The vellum is made to pafs from right to left, behind the tube of the thermometer, and to graze along its furface. The obferver, to find the corrections to be made, pulls out the vellum till the fcale corresponding to the obferved altitude of the barometer comes to touch the thermometer, and on that fcale he counts them. The vellum is then let go, and the fcrew gently furls it up. 40 His operaThe author having now, as he imagined, completely tions on the finished the inftruments neceffary for the accurate menfuration of heights; proceeded to establish, by experiment, the altitudes correfponding to the different defcents of the mercury. Much had been written, and many rules had been given, on this fubject, by different eminent philofophers, fince the days of Pafcal, who firft broached it: but thefe difagreed fo much with one another, and prefented fo little good reafon why any one of them fhould be preferred, that no conclufion could with confidence be deduced from them. It became requifite, therefore, to lay them all afide, and to endeavour to discover by practice what could not be afcertained by theory. Salève, a mountain near Geneva, was chofen for the fcene of thefe operations. This mountain is near 3000 French feet high. The height of it was twice measured by levelling, and the refult of the menfurations differed only 10 inches; though there intervened fix months between them, and the 41 the baro meter at Little progress was made in this plan, when a phe- Strange a nomenon, altogether unexpected, presented itself. The "omalies of barometer being obferved, at one of the stations, twice in one day, was found to ftand higher in the latter ob- different fervation than in the former. This alteration gave times of little furprife, because it was naturally imputed to a the day. change of the weight of the atmosphere, which would affect the barometer on the plain in the fame manner. But it produced a degree of aftonishment, when on examining the ftate of the latter, it was found, instead of correfponding with the motions of the former, to have held an oppofite courfe, and to have fallen while the other rofe. This difference could not proceed from any inaccuracy in the obfervations, which had been taken with all imaginable care; and it was fo confiderable as to deftroy all hopes of fuccefs, fhould the caufe not be detected and compensated. The experiment was repeated feveral times, at in. tervals, that no material circumftance might efcape notice. An obferver on the monntain, and another on the plain, took their respective stations at the rifing of the fun, and continued to mark an observation, every quarter of an hour, till it fet. It was found, that the lower barometer gradually defcended for the first three quarters of the day; after which it reafcended, till in the evening it ftood at nearly the fame height as in the, morning. While the higher barometer afcended for the first three fourths of the day; and then defcended, fo as to regain likewife, about fun-fet, the altitude of the morning. 42 The following theory feems to account in a fatis. Accounted factory manner for this phenomenon. When the fun for. rifes above the horizon of any place, his beams penetrate the whole of the fection of the atmofphere of which that horizon is the base. They fall, however, very obliquely on the greater part of it, communicate little heat to it, and confequently produce little dilatation of its air. As the fun advances, the rays be come 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 fun is in the meridian. It increases while the place receives more rays than it loses, which it will do for a confiderable time after mid-day; in like manner as the tide attains not its higheft altitude till the moon has advanced a confiderable way to the weft of the meridian. The heat of the atmosphere is greateft at the furface of the earth, and feems not to afcend to any great di ftance above it. The dilatations, for this reafon, of the air, produced by the fun, will be found chiefly, if not folely, 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 themfelves vertically, will become longer, and at the fame time fpecifically lighter, in confequence of the rarefaction of their inferior parts. The motion of Barometer. air, till it rifes into wind, is not rapid: thefe lengthened columns, therefore, will take fome time to diffipate their fummits among the adjacent lefs rarefied columns that are not fo high; at leaft, they will not do this as faft as their length is increased by the rarefac 43 meters ne tion of their bases. The reader, we prefume, anticipates the application of this theory to the folution of the phenomenon in question. The barometer on the plain begins to fall a little after morning, becaufe the column of air that fupports it becomes fpecifically lighter on account of the rarefaction arifing from the heat of the fun. It continues to fall for the firft three quarters of the day; because, during that time, the heat, and confequently the rarefaction, are gradually increafing. It rifes again, after this period: because the cold, and of courfe the condenfation, coming on, the fpecific 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 rifes after morning, and continues to do fo for three-fourths of the day, for two reafons. The denfity of the columns of air is greatett near the earth, and decreases as the distance from it increafes. The higher, for this reafon, we afcend in the atmosphere, we meet with air fpecifically lighter. But by the rarefaction of the bafe of the column that fupports the mercury of the barometer on the eminence, the denfer 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 preffed with a weight, nearly as great as it would fuftain, were it brought down, in the atmosphere, to the natural place of that denfer air now raised above it by the prolongation of the bafe of the column. The other reafon is, that as the rarefaction does not take place at any great diftance from the earth, little change is produced in the specific gravity of the portion of the column that preffes on the higher barometer, and the fummit of that column diffipates itself more flowly than it increases. Thus, we fee how this barometer must ascend during the first three fourths of the day, and purfue a course the reverfe of that on the plain. The condenfations returning after this time, the denfer air fubfides, the equilibrium takes place, and the mercury defcends to its firft pofition. This phenomenon prompted the idea of a fecond pair other pair of thermometers, to measure the mean heat of the coof thermo- lumn of air intercepted between the barometers. Thefe thermometers are extremely delicate and fenfible. The scilary. tubes are the fineft capillary, the glafs very thin, and the diameters of the balls only three lines. The balls are infulated, or detached from the feales, which are fixed to the tubes only, by ligatures of fine brafs-wire covered with filk. The air, by this contrivance, has free communication with the balls on all fides; and, if the direct rays of the fun be intercepted at fome diftance by a bit of paper, or even the leaf of a tree, the thermometers will quickly mark the true temperature the altitudes from the defcents of the mercury. He Barometer. The altitudes are computed by logarithms. A table To apply this table to the prefent purpose: let us fuppofe the whole atmosphere divided into concentric spherical fections, whofe common centre is that of the earth. Suppofe also all these sections of equal thicknefs, namely, 12.497 toifes, which is found to be the thickness of the loweft fection, and balances a line of mercury, when the barometer ftands at 348 lines or 29 inches. Add, then, all these fections together; and we fhall have the total altitude of the atmosphere expreffed in an arithmetical progreffion, whofe common difference is 12.497 toifes. Confequently, in this view, the heights are proportioned to the logarithma. It remains only to find the defcents of the mercury, which meafures the weights of the refpective fections, in geometrical proportion, in order to justify the application of the logarithmic table to the computation of the altitudes. Now, it is eafy to prove, in a very fatisfactory manner, that the mean denfities of thefe fections, which are in proportion of their weights, muft be in geometrical progreffion, when the altitudes are in arithmetical; confequently, it is with great propriety and convenience that the logarithms are employed in the computation of the altitudes correfponding to the defcents of the mercury. For, to find the vertical diftance between two barometers, at different heights, no more is neceffary than to look, in a table of logarithms, for the numbers that express in lines, or fixteenths of a line, the altitudes of the two columns of mercury, and take the logarithms of thefe numbers, whofe difference will give this diflance accurately, in thoufandth parts of a toife. Multiply the toifes by 6, which will furnish the altitudes in French feet. The author made about 500 different observations at the feveral ftations on the mountain of Salève, which both fuggefted and verified the computation by logarithms. Many, however, of thefe obfervations, produced conclufions that deviated confiderably from the refult3 of the actual menfuration, on account of the dif ferent temperatures in which they were taken. It was the defign of the fecond pair of thermometers to point out the corrections of thefe deviations. In fettling the fcales neceffary for this end, the first object was, to mark the temperature of all the obfervations where the logarithms gave the altitudes exactly, or nearly equal to what they were found to be by levelling. This temperature correfponded to 163 on the fcale of Reaumur, and to 70 on that of Fahrenheit, and as it was fixed. the term o. The next ftep was, to determine the corrections of the heights that became neceffary, accord ing |