BAROMETER, the instrument by which the weight or pressure of the atmosphere is estimated, The barometer was invented by Torricelli, a pupil of Galileo, in 1613. It had shortly before been found, in attempting to raise water from a very deep well near Florence, that, in spite of all the pains taken in fitting the piston and valves, the water could by no effort be made to rise higher in the pump than about 32 feet. This remarkable phenomenon Torricelli accounted for by attributing pressure to the air. He reasoned that water will rise in a vacuum only to a certain height, so that the downward pressure or weight of the column of water will just balance the pressure of the atmosphere ; and he further argued that if a fluid heavier than water be used it will not rise so high in the tube as the water. To prove this, he selected a glass tube about a quarter of an inch in diameter and 4 feet long, and hermetically sealed one of its ends ; he then filled it with mercury and, applying his finger to the open end, inverted it in a basin containing mercury. The mercury instantly sank to nearly 30 inches above the surface of the mercury in the basin, leaving in the top of the tube an apparent vacuum, which is, indeed, one of the most perfect that can yet be produced, and is called after this great experimenter, the Torricellian vacuum. He next converted the mercurial column into a form suited for observation by bending the lower end of the tube, thus constructing what has since been called the siphon barometer. The fundamental principle of the barometer cannot be better illustrated than by his experiment (see fig. 2). In truth, a scale is all that is required to render this simple apparatus a perfect barometer.

The heights of the columns of two fluids in equilibrium are inversely as their specific gravities ; and as mercury is 10,784 times heavier than air, the height of the atmosphere would be 10,784 times 30 inches, or nearly five miles, if it were composed of layers equally dense throughout. But since air becomes less dense as we ascend, owing to its great elasticity and the diminished pressure, the real height of the atmosphere is very much greater. From observations of luminous meteors, it has been inferred that the height is at least 120 miles, and that, in an extremely attenuated form, it may even considerably exceed 200 miles.

Various fluids might be used in constructing barometers. If water were used, the barometric column would be about 35 feet long. The advantages, however, which water barometers might be supposed to possess in showing changes of atmospheric pressure on a large scale, are more than counterbalanced by a serious objection. The space in the tube above the column of water is far from being a vacuum, being filled with aqueous vapour, which presses on the column with a force varying with the temperature. At a temperature of 32° Fahr. the column would be depressed half an inch, and at 75° a foot. Since in mercurial barometers the space at the top of the column is one of the most perfect vacuums that can be produced, the best fluid for the construction of barometers is mercury. It is therefore the only fluid used where scientific accuracy is aimed at. Pure mercury must be used in filling the tubes of barometers ; because if it be impure, the density will not be that of mercury, and, consequently, the length of the columns will not be the same as that of a column composed of pure mercury alone. Even should the density happen to be the same as that of pure mercury the impurities would soon appear, impeding the action of the fluid as it rises and falls, and thus rendering the instrument unfit for accurate observation. In filling barometer tubes, air and moisture get mixed with the mercury, and must be expelled by boiling the mercury in the tube. It being essential that the mercury be quite freed from air and moisture, no barometer should be used till it has been well ascertained that this has been done. Some time after the instrument has been hung in an observing position, let it be inclined gently and with care, so that the mercury may strike against the top of the glass tube ; if there is no air within, a sharp metallic click will be heard, but if the sound is dull, the air and moisture have not been entirely expelled. If the mercury should appear at any time to adhere somewhat to the tube and the convex surface assume a more flattened form, it may be concluded that air or moisture is present. If on examining the mercury with a lens minute bubbles are visible, air is present. In all these cases the instrument must be rectified.

The best barometers are usually fitted with en air-trap, originally proposed by Gay-Lussac for the purpose of arresting the ascent to the Torricellian vacuum of any air that may have found its way into the column by the cistern. The air-trap is fitted into the tube somewhere between the scale and the cistern, Barometers furnished with an air-trap can be conveyed from place to place with more safety, and they remain longer in good working order.

There are two classes of barometers - Siphon, Barometers and Cistern Barometers. The Siphon .Barometer (fig. 1) consists of a tube bent in the form of a siphon, and is of the same diameter throughout. A graduated scale passes along the whole length of the tube, and the height of the barometer is ascertained by taking the difference of the readings of the upper and lower limbs respectively. 'Phis instrument may also be read b1 bringing the zero-point of th( graduated scale to the level o: the surface of the lower limb b1 means of a screw, and reading off the height at once from the surface of the upper limb. Thi: barometer requires no correctior for errors of capillarity or capes city. Since, however, impurities are contracted by the mercury ir the lower limb, which is usually in open contact with the air, tilt satisfactory working of the instill. went comes soon to be seriously interfered with.

Fig. 2. shows the Cistern Barometer in its essential and its simplest form. This barometer is subject to two kinds of error, the one arising from capillarity, and the other from changes in the level of the surface of the cistern as the mercury rises and falls in the tube, the latter being technically called the error of capacity. if a glass tube of small bore be plunged into a vessel containing mercury, it will be observed that the level of the mercury in the tube is not in the line of that of the mercury in the vessel, but somewhat below it, and that the surface is convex. The capillary depression is inversely proportional to the diameter of the tube. If the diameter of the tube be 0.1 inch, the capillary depression of mercury in boiled tubes, or error of capillarity, is 0.070 inch ; if 0.2 inch, the error is 0.029 inch ; if 0.3 inch, it is 0-014 inch ; and if 0.5 inch, it is only 0-003 inch. Since capillarity depresses the height of the column, cistern barometers require an addition to be made to the observed height, in order to give the true pressure, the amount depending, of course, on the diameter of the tube.

The error of capacity arises in this way. The height of the barometer is the perpendicular distance between the surface of the mercury in the cistern and the upper surface of the mercurial column. Now, when the barometer falls from 30 to 29 inches, an inch of mercury must flow out of the tube and pass into the cistern, thus raising the cistern level ; and, on the other hand, when the barometer rises, mercury must flow out of the cistern into the tube, thus lowering the level of the mercury in the cistern. Since the scales of barometers are usually engraved on their brass cases, which are fixed (and, consequently, the zero-point from which the scale is graduated is also fixed), it follows that, from the incessant changes in the level of the cistern, the readings would be sometimes too high and sometimes too low, if no provision were made against this source of error.

A. simple way of correcting the error of capacity is - to ascertain (1) the neutral point of the instrument, or that height at which the zero of the scale is exactly at the height of the surface of the cistern, and (2) the rate of error as the barometer rises or falls above this point, and then apply a correction proportional to this rate. In many of the barometers used on the Continent the surface area of the cistern is 100 times greater than that of the tube, in which case the error is small, and ean, besides, be easily calculated. This is a good barometer for ordinary observers, inasmuch as no error arises in bringing the surface of the mercury of the cistern to the zero-point of the scale, which one requires to have some skill as a manipulator and good light to do correctly. Another way of getting rid of this error is effected by the Board of Trade Barometer, constructed originally by Adie of London. In this barometer the error of capillarity is allowed for in fixing the zero-point of the scale, and the error of capacity is obviated by making the scale-inches not true inches, but just so much less as exactly to counterbalance the error of capacity.

But the instrument in which the error of capacity is satisfactorily (indeed, entirely) got rid of is Fortin' s Barometer. Fig. 3 shows how this is effected. The cistern is formed of a glass cylinder, through which the level of the mercury may be seen. The bottom is made like a bag, of flexible leather, against which a screw works. At the top of the interior of the cistern is a small piece of ivory, the point of which coincides with the zero of the scale. By means of the screw, which acts on • the flexible cistern bottom, the level of the mercury can be raised or depressed so as to bring the ivory point exactly to the surface of the mercury in the cistern. In some barometers the cistern is fixed, and the ivory point is brought to the level of the mercury in the cistern by raising or depressing the scale.

What is called the Fitzroy Barometer is only a modified form of the siphon barometer, with the lower limb blown into a moderately-sized bulb, resembling a cistern in some respects, and thus giving a larger range to the readings of the upper limb. It is only suited for popular, not for scientific purposes. The common Wheel Barometer, the popular form of the weather glass, is also a modification of the siphon barometer. A small weight, glass or iron, floats on the mercury in the lower limb; to this weight a thread is attached, which is led round a horizontal axis, a small weight being suspended at its free extremity to keep it tight. The float rises and falls with the fluctuations of the barometer, and a pointer fixed to a horizontal axis being turned by this means indicates the height of the barometer by figures on a dial. Since the mercury only rises or falls in the open end of the siphon to the extent of half the oscillation, a cistern is added to the top of the upper limb to increase the amount of the oscillation in the lower limb. This form of the barometer is only suited for very rough purposes, since large and uncertain errors arise from the shortening and lengthening of the thread with the varying dampness or dryness of the air, and from the friction of the different parts of the mechanism of the instrument.

Since in working out the great atmospheric problem of the force of the wind in its relation to the barometric gradient (i.e., the differences of the pressures at different places, reduced to the same level) readings from about the hundredth of an inch (0.010), or even less, require to be obssrved and stated with great accuracy, the extreme importance of accurate sensitive barometers will be apparent, - instruments not only possessing a great range of scale, but a scale which will truly indicate the real atmospheric pressure at all times. The two barometers which best satisfy this requirement are King's Barometer, which has been in use for many years at the Liverpool Observatory, and Howson's Barometer. Fig. 4 shows the essential and peculiar parts of Howson's barometer. A is the barometer tube, which is of large diameter, and longer than ordinary in order to admit of a greater length of range. B is a movable cylindrical cistern, having attached to its bottom a long hollow tube or stalk c, hermetically sealed, springing to a height of about 28 inches above the fixed level of the mercury in the cistern. This stalk terminates a little below the upper level of the mercury, and its upper end is thus exposed to no more downward pressure than that of the mercury above it ; consequently, there is an excess of upward pressure of the air which tends to raise the cistern. When the excess of upward pressure is exactly balanced by the weight of the cistern with its stalk and contained mercury up to b, an equilibrium will be established, which will keep the apparatus stationary or hanging in suspension. If now the atmospheric pressure acting on the cistern be increased, and if the thickness of the glass tube A be supposed to be nothing, the cistern would continuo to ascend to an indefinite extent, since there is nothing to stop it. But as the glass is a substance of some thickness, mercury is displaced by the glass as it is plunged further into the cistern ; and as it thus offers a resistance to the ascent of the cistern, the cistern will come to rest when the quantity of mercury displaced is equi

The liability of the barometer to be broken in carriage is great. This risk is considerably lessened in the Board of Trade Barometer, which has the tube very much reduced in diameter for a part of its length, breakage from " pumping " being so much lessened thereby that the instrument may be sent as a parcel by rail, if only very ordinary care be taken in the carriage. This is essentially the principle of the Harine Barometer, which., however, has the tube still more contracted. For rougher modes of transit an ingeniously constructed iron barometer has been invented by Mr T. Stevenson, C.E.

The sympiezometer was invented by Adie of Edinburgh. It consists of a glass tube, with a small chamber at the top and an open cistern below. The upper part of the tube is filled with air, and the lower part and cistern with glycerine. When atmospheric pressure is increased, the air is compressed by the rising of the fluid; but when it is diminished the fluid falls, and the contained air expands. To correct for the error arising from the increased pressure of the contained air when its temperature varies, a thermometer and sliding-scale are added, so that the instrument may be adjusted to the temperature at each observation. It is a sensitive instrument, and well suited for rough purposes at sea and for travelling, but not for exact observation. It has been for some time superseded by the Aneroid, which far exceeds it in handiness, portability, and correctness. The Aneroid Barometer was invented by Vidi, and patented in England in 1844. Its action depends on the effect produced by the pressure of the atmosphere on a circular metallic chamber partially exhausted of air and hermetically sealed. Fig. 5 represents the internal construction, as seen when the face is removed, but with the hand still attached. a is a flat circular metallic box, having its upper and under surfaces corrugated in concentric circles. This box or chamber being partially exhausted of air, through the short tube b, which is subsequently made air-tight by soldering, constitutes a spring, which is affected by every variation of pressure in the external atmosphere, the corrugations on its surface increasing its elasticity. At the centre of the upper surface of the exhausted chamber there is a solid cylindrical projection x, to the top of which the principal lever cde is attached, as shown in the drawing. This lever rests partly on a spiral spring at d; it is also supported by two vertical pins, with perfect freedom of motion. The end e of the lever is attached to a second or small lever!, from which a chain g extends to h, where it works on a drum attached to the axis of the hand, connected with a hair spring at II, changing the motion from vertical to horizontal, and regulating the hand, the attachments of which are made to the metallic plate i. The motion originates in the corrugated elastic box a, the surface of which is depressed or elevated as the weight of the atmosphere is increased or diminished, and this motion is communicated through the levers to the axis of the hand at h. The spiral spring on which the lever rests at d is intended to compensate for the effects of alterations of temperature. The actual movement at the centre of the exhausted box, from whence the indications emanate, is very slight, but by the action of the levers this is multiplied 657 times at the point of the hand, so that a movement of the 220th part of an inch in the box carries the point of the hand through three inches on the dial. The effect of this combination is to multiply the smallest degrees of atmospheric pressure, so as to render them sensible on the index.

The instrument requires, however, to be repeatedly compared with a mercurial barometer, being liable to changes from the elasticity of the brass chamber changing, or from changes in the system of levers which work the pointer. Though aneroids are constructed showing great accuracy in their indications, yet none can lay any claim to the exactness of mercurial barometers. The mechanism is liable to get fouled and otherwise go out of order, so that they may change 0.300 inch in a few weeks, or even indicate pressure so inaccurately and so irregularly that no confidence can be placed in them for even a few days, if the means of comparing them with a mercurial barometer be not at hand.

Of the self registeringbarometers, the best are those which accomplish this object by photography. This is done by • concentrating the rays of a gas flame by means of a lens, so that they strike the top of the mercurial column. A sheet of prepared paper is attached to a frame placed behind a screen, with a narrow vertical slit in the line of the rays. The mercury being opaque throws a part of the paper in the shade, while above the mercury the rays from tho flame pass unobstructed to the paper. The paper being carried steadily round on a drum at a given fate per hour, the height of the column of mercury is photographed continuously on the paper. From the photograph the height of the barometer at any instant may be taken. King's, Hardy's, lie tqh's, Hipp's, and Thorell's self-registering barometers may also be referred to as giving continuous records of the pressure. In all continuously registering barometers, however, it is necessary, as a check, to make eye-observations with a mercury standard barometer hanging near the registering barometer from four to eight times daily, In constructing the best barometers three materials are employed, viz. : - (1) brass, for the case, on which the scale is engraved ; (2) glass, for the tube containing the mercury ; and (3) the mercury itself. Brass is the best material for the case and scale, inasmuch as its co-efficient of expansion is well known, and is practically the same though the alloy be not in all eases exactly alike. It is evident that if the co-efficient of expansion of mercury and brass were the same, the height of the mercury as indicated by the brass scale would be the true height of the mercurial column. But this is not the case, the co-efficient of expansion for mercury being considerably greater than that for brass. The result is that if a barometer stand at 30 inches when the temperature of the whole instrument, mercury and brass, is 32°, it will no longer stand at 30 inches if the temperature be raised to 69°; in fact, it will then stand at 30.1 inches. This increase in the height of the column by the tenth of an inch is not due to any increase of pressure, but altogether to the greater expansion of the mercury at the higher temperature, as compared with the expansion of the brass case with the engraved scale by which the height is measured. In order, therefore, to compare with each other with exactness barometric observations made at different temperatures, it is necessary to reduce them to the heights at which they would stand at some uniform temperature. The temperature to which such observations are now almost everywhere reduced is 32° Fahr.

The following is Schumacher's formula for computing the corrections for barometers, whose heights are noted in English inches, for temperature t, according to Fahrenheit's scale : - n(t - 32°) - s(t - 62') 1+ ni(t - 32') where h = height of barometer, s = expansion of brass for 1° Fahr. = 0.00001041.

The standard temperature of the English yard being 62' and not 32°, it will be found in working out the corrections from the above formula that the temperature of no correction is not 32° but 28°•5. If the scale be engraved on the glass tube, or if the instrument be furnished with a glass scale or with a wooden scale, different corrections are required These may be worked out from the above formula by substituting for the co-efficient of the expansion of brass that of glass which is assumed to be 0.00000498, or that of wood, which is assumed to be 0. Wood, however, should not be used, its expansion with temperature being° unsteady, as well as uncertain.

If the brass scale be attached to a wooden frame and be free to move up and down the frame, as is the case with many siphon barometers, the corrections for brass scales are to be used, since the zero-point of the scale is brought to the level of the lower limb ; but if the brass scale be fixed to a wooden frame, the corrections for brass scales are only applicable provided the zero of the scale be fixed at (or nearly at) the zero line of the column, and be free to expand upwards. In siphon barometers, with which an observation is made from two readings on the scale, the scale must be free to expand in one direction. Again, if only the upper part of the scale, say from 27 to 31 inches, be screwed to a wooden frame, it is evident that not the corrections for brass scales, but those for wooden scales must be used. No account needs to be taken of the expansion of the glass tube containing° the mercury, it being evident that no correction for this expansion is required in the case of any barometer the height of which is measured from the surface of the mercury in the cistern.

In fixing a barometer for observation, it is indispensable that it be hung in a perpendicular position, seeing that it is the perpendicular distance of the surface of the mercury in the cistern and that of the top of the column which is the true height of the barometer. Hence it is desirable that the barometer swing in position ; or if this be attended with risk or inconvenience, it must be seen that it be clamped or permanently fixed in a position exactly vertical. The surface of the mercurial column 1.3 convex, and in noting the height of the barometer, it is not the chord of the curve, - an error not unfrequently made, - but its tangent which is taken. This is done by setting the straight lower edge of the vernier, an appendage with which the barometer is furnished, as a tangent to the curve. The vernier is made to slide up and down the scale, and by it the height of the barometer may be read true to 0.002 or even to 0.001 inch. See VERNIER.

In hanging a barometer the following points should be attended to : - (1), That it be hung so that the mercurial column be quite perpendicular ; (2), that the scale be about 5 feet high, for facility of reading ; (3), that the whole instrument, particularly the scale and the cistern, be hung in a good light ; and (4), that it be hung in a position in which it will be exposed to as little fluctuation of temperature as possible. A. wall heated by a flue, and positions which expose the instrument to the heat of the sun or to that of a fire, are very objectionable. It is to be kept in mind that no barometric observation can be regarded as good unless the attached thermometer indicates a temperature differing from that of the whole instrument not more than a degree. For every degree of temperature the attached thermometer differs from the barometer, the observation will be faulty to the extent of about 0.003 inch, which in discussions of diurnal range, barometric gradients, lunar range, and many other questions, is a serious amount.

Before being used, barometers should be thoroughly examined as to the state of the mercury, the size of cistern (so as to admit of low readings), and their agreement with some known standard instrument at different points of the scale. The pressure of the atmosphere is not expressed by the weight of the mercury sustained in the tube by it, but by the perpendicular height of the column. Thus, when the height of the column is 30 inches, it is not said that the atmospheric pressure is 14.7 lb on the square inch, or the weight of the mercury filling a tube at that height whose transverse section equals a square inch, but that it is 30 inches, meaning that the p•esaire will sustain a column of mercury of that height.

The height of the barometer is expressed in English inches in England and America. In France and most European countries, the height is given in millimetres, a millimetre being the thousandth part of a metre, which equals 39.37079 English inches. Up to 1869 the barometer The decisive experiment by which Pascal established the reality of atmospheric pressure suggested to him the method of measuring heights by means of the barometer. The first attempts to effect this were necessarily rude and inaccurate, since they went on the assumption that the lower mass of air is of uniform density. The discovery, however, of the actual relation subsisting between the density of air and its elasticity by Boyle in England, and about the same time by Mariotte in France, laid a sure foundation for this branch of atmospheric physics - the relation being that, at the same temperature, the pressure of a gas is exactly proportional to its density.

The truth of this law may be shown by the following experiment. Take a glass tube, of equal bore throughout, closed at one end, and bent in the form of a siphon (fig. I), and let us suppose that it contains in the closed limb a portion of air AB, shut off from the atmosphere by mercury filling the lower portion of the tube, and that the enclosed portion of air exists at the ordinary pressure of the atmosphere or 30 inches. In this case the mercury in each limb, being subject to the same pressure, will stand at the same level. If we now pour mercury into the long limb (fig. 2) till the level in this limb stands 30 inches above the level in the closed limb, the additional mercury will tend to compress the air in A'B' with a pressure equal to that exerted by a column of 30 inches of mercury. In the latter case, therefore, the air is subjected to a pressure of two atmospheres, or GO inches, while in the former it was only subjected to a pressure of one atmosphere or 30 inches. It will be found that the space A'B' under the pressure of two atmospheres is only half the space AB where the pressure is only one atmosphere. If mercury had been filled in till the difference of level of the mercury in the two limbs was GO inches, or a pressure of three atmospheres, the space occupied by the air in the closed limb would have been only a third of the original space when the pressure was only that of one atmosphere. Generally, Boyle's law or Mariotte's law is this : - The volume of a gas varies inversely as the pressure. Since the same quantity of air has been experimented with, it follows that the density is doubled with a pressure of two atmospheres, and trebled with that of three, and hence the pressure of a gas is proportional to its density.

This law, however, only holds provided the temperature is the same. The familiar illustration of a bladder, partially filled with air, expanding on being placed near a fire, shows that if the pressure remains the same, - the pressure in this ease being that of the atmosphere, - the gas will occupy a larger space if its temperature be raised. If the temperature be increased and the air be confined so as to occupy the same space, the pressure will be increased.

The relation between the temperature and pressure of gases was first discovered by Gay-Lussac; and more recently our knowledge of this branch of the subject has been greatly enlarged by the beautiful and accurate experiments of Regnault. From those experiments it has been concluded that the co-efficient which denotes increase of elasticity for I° Fahr. of air whose volume is constant equals '002036; and that the co-efficient which denotes increase of volume for 1° Fahr. of air whose elasticity is constant equals .002039. It may further be added that the co-efficient of expansion for carbonic acid gas, hydrogen, and all other gases, is as nearly as possible the same.

When a fluid is allowed to evaporate in the exhausted receiver of an air-pump, vapour rises from it until its pressure reaches a certain point, after which all further evaporation is arrested. This point depends on the nature of the fluid itself and on the temperature, and it indicates the greatest vapour pressure possible for the fluid at the particular temperature. Regnault has shown the amount of the vapour pressure of wateratdifferent temperatures, thus - Temp. Max. Pressure Temp. Jinx. Pressure Fahr. of Vapour. Fahr of Vapour inch. inch.

00.0l4 60 0.361 If gases of different densities be put into the same vessel it is found that they do not arrange themselves according to their densities, but are ultimately diffused through each other in the most intimate manner. Each gas tends to diffuse itself as in a vacuum, the effect of the presence of other gases being merely to retard the process of their mutual diffusion. As regards the atmosphere, evaporation goes on until the maximum vapour pressure for the temperature has been attained, at which point the air is said to be saturated, and whilst the temperature remains the same further evaporation is arrested. Thus, at a tempera, ture of 50° evaporation goes on until the vapour pressure reaches 0361 inch, but if the temperature were raised to GO' the process of evaporation would be renewed, and go on till the vapour pressure rose to 0.518 inch. If at a vapour pressure of 0.518 inch the temperature were to fall from 60° to 50°, the air would no longer be capable of retaining the whole of the aqueous vapour in suspension, but the surplus part would be condensed and fall as rain. In the change from the aeriform to the liquid state a quantity of latent heat is given out. The yet uncertain effect of these changes, particularly the change of form from the aeriform to the liquid state, on the pressure, temperature, and movements of the air, renders it peculiarly desirable that barometeric observations for the determination of was given in half-lines in Russia, which, equalling the twentieth of an English inch, were readily reduced to English inches by dividing by 20. The metric barometric scale is now used in Russia. In a few countries on the Continent the French or Paris line, equalling 0.088814 inch, still continues to be used. Probably millimetre and English inch scales will soon be exclusively in use. The English measure of length being a standard at 62° Fahr., the old. French measure at 61°.2, and the metric scale at 32', it is necessary, before comparing observations made with the three barometers, to reduce them to the same temperature, so as to neutralize the inequalities arising from the expansion of the scales by heat.

The barometer is a valuable instrument as an indicator of coming weather, provided its readings be interpreted with intelligence. High pressures generally attend fine weather, but they not unfrequently accompany wet stormy weather ; on the other hand, low pressures, which usually occur with wet and stormy weather, not unfrequently accompany fine mild weather, particularly in winter and in the northern parts of Great Britain. The truth is, the barometer merely indicates atmospheric pressure directly, whilst it indicates weather only inferentially. The chief points to be attended to are its fluctuations taken in connection with the wind and the state of the sky, but above all, the readings of the barometer as compared with those at neighbouring places, since it is difference of pressure, or the amount of the barometric gradient, which determines the strength of the wind and the weather generally.

heights should not be made when clouds are forming or rain is falling.

Dalton has shown 1 that air charged with vapour is specifically lighter than when it wants the vapour ; in other words, the more vapour any given qua:rtity of air has in it the less is its specific gravity ; and Sir William Thomson has shown 2 that the condensation of vapour in ascending currents of air is the chief cause of the cooling effect being so much less than that which would be experienced by dry air. From these ascertained effects of aqueous vapour in modifying the pressure and temperature of the atmosphere, the importance in the barometric measurement of heights of full and accurate observations of the hygrometry of the atmosphere and of the weather will be v.pparent.

Since the equilibrium of the vapour atmosphere is being constantly disturbed by every instance of condensation, by the ceaseless process of evaporation, and by every change of temperature, and since the presence of oxygen and nitrogen greatly obstructs the free diffusion of the aqueous vapours, it follows that Dalton's law of the independent pressure of the vapour and the dry air does not absolutely hold good. From the constant effort of the vapour to attain to a state of equilibrium there is, however, a continual tendency to approach this state. Since the equal diffusion of the dry air and the vapour is never reached, observations can only indicate local humidity, and therefore as regards any considerable stratum of air can only be regarded as approximate. Though particular observations may often indicate a humidity wide of the mark, yet in long averages a close approximation is reached, except in confined localities which are exceptionally damp or dry. Bence in observations for the determination of heights, the results of a long-continued series of observations should be employed, and those hours should be chosen whose mean is near the daily mean.

The most recent results arrived at by Regnault are the best, but it is to be regretted that the whole subject of the hygrometry, both as regards the methods of observation and the methods of discussing the observations, is still in an unsatisfactory state. This consideration, taken in connection with our defective knowledge of the relation of aqueous vapour to radiant heat, of the mode of its diffusion both vertically and horizontally, and of the influence exerted by its condensation into cloud and rain, and with our ignorance of the merely mechanical effects of ascending, descending, and horizontal currents of air in increasing or diminishing barometric pressure, renders it evident that heights deduced from barometric observations can only be regarded as approximate. It is much to be desired, in stating results, that the limit of error were taken into account, and the nearest round number in accordance therewith should alone be given as the calculated result. Thus, it is a mistake to give as the height of a place 1999 feet when the calculation is based wholly on barometric observations, and the limit of error amounts to 30 feet or more. The height 2000 should be given as the result.

The correction for decrease of gravity at the higher station, as compared with the force of gravity at the lower station or at ea-level, must also be taken into .account. Its amount is small, being, roughly speaking, only about 0.001 inch per 400 feet. Sincethe force of gravity is diminished in proportion to the square of the distance from the centre of gravity, the rate of its decrease with the height varies in different latitudes. Places at the equator being farther from the earth's centre than places at the poles, it follows that the force of gravity diminishes at a less rapid rate as we ascend at the equator than it does at the poles. Now, since at the equator gravity diminishes less rapidly with the height, the air at any given height will exert a higher pressure there than anywhere else on the globe at the same height as compared with what it does at the sea-level of the latitude. Hence a subtraction requires to be made at the equator, and the amount to be subtracted diminishes as we proceed into higher latitudes, till it falls to zero at latitude 45°, where the force of gravity is assumed to be the mean. For higher latitudes an addition is required which constantly increases till it reaches the maximum at the poles. This correction is also small, being for 1000 feet less than 0.001 inch in Great Britain, and less than 0.003 at the equator and the poles.

Various formula), for the barometrical measurement of heights, based on these principles, have been, given by Laplace and others, not a few of them being unnecessarily refined and intricate when the real character of the data is taken into consideration. The following formula by Etildniann 3 is given as the simplest and best, being based on the most recent results which have been arrived at : - in which h is the difference in metres of level between the two stations ; t' and t" the temperature centigrade of the air at the two stations ; b' and 5" the heights of the barometer in millimetres, corrected for temperature and for all instrumental errors ; 02 and u" the elastic force of vapour ; the mean of the latitudes of the two stations ; and z the height of the lower station above the sea. Making Riihlinann has calculated the values A, C, D, and E for the different values of the respective arguments, which are given in the tables appended to the work.

From formula (1) we obtain - It is assumed that the whole stratum of air between the two heights is in a state of rest, and that the means of the temperature and humidity observed at the two stations are the means respectively of the stratum of air between them.

If great accuracy is desired, both barometers must be read from the zeros of their scales, and the observations must be corrected for all merely instrumental errors, and must be made strictly at the same time or times, seeing that a very small error, arising either from imperfect observations, or from their not being comparable, produces a comparatively large error in the calculated results.

In deducing heights from long-continued observations it should be ascertained that the barometers and observations are good, and observations should if possible be used which have been made at the same hours of the day and during the same years. Observations at different hours of the day are not comparable, since, owing to our imperfect knowledge of the differences of daily barometric range, the necessity for the application of any so-called corrections for daily range must necessarily lead to error. The comparison should also only be between observations made during the same years, since the means of different years often differ widely from each other. Thus the difference of height between two places at which barometrical observations were made, from 1830 to 1859 and from 1850 to 1869 respectively, could be more accurately ascertained from the ten years' averages from 1850 to 1859 during which observations were made at both places, than from the longer averages of thirty and twenty years. Inattention to this point has often led to error, especially in eases where at one of the places only a few years were available. To secure greater accuracy, the calculations should be made on the mean for the year, the two extreme months, January and July, and that month during which the distribution of pressure is most uniform over the region where the places are situated. Owing to the great differences in the distribution of atmospheric pressure in different parts of the globe (see ATMOSPHERE), comparison of the observations at the higher station with those at more than one lower station is in some cases indispensable. Thus, if it were desired to compute the height of Dovre, in Norway, barometrically, it should be compared both with Christiania and with Christiansund on the west coast ; for if compared with Christiania alone the calculated height would be too high, and if with Christiansund too low, the reason being that the mean annual pressure diminishes from Christiania to Christiansund. The same remark applies to a large portion of Hindustan and to many other regions of the globe.

The more special precautions to be taken in deducing heights from one or a few observations, that is, from such data as travellers observe, are these : - that the observations be made in as settled weather as possible, at those hours of the clay, at least, at which observations are made at the nearest meteorological stations, and be repeated as long as possible from day to day ; that the barometer hang perpendicularly and in shade ; and that the observations be not made till the whole instrument has acquired the temperature of the surrounding air. For, for every degree which the temperature indicated by the attached thermometer differs from the temperature of the whole instrument, there is an error of about 0.003 inch.

From their portability and handiness the aneroid barometer, and the thermometer for ascertaining the point at which water boils, arc of great use in determining heights, - the thermometer, if properly managed, being the more accurate of the two. Since, owing to the sluggishness with which the aneroid often follows the changes of pressure, espe- cially low pressures, its readings should not be recorded till it has hung for some hours at the place of observation, and if this be not possible, the time which elapsed from arriving at the place and making the observations should be stated. It may not be unnecessary to add that every opportunity which presents itself should be taken of comparing it with a standard mercurial barometer, owing to the variations, irregular or permanent, to which aneroids are subject, and that the instrument should always be read in one position, since the difference between the reading in a horizontal position and the reading in a vertical position is often considerable.

At a pressure of 29.905 inches distilled water boils at 212°. The temperature of the boiling point varies with the nature of the vessel. Thus, if the interior of the glass vessel be varnished with shell-lac, the temperature may rise to 221°; and if iron filings be dropped into the water, the temperature is lowered. But in all these cases the temperature of the vapour arising from the water is as nearly as possible the same. Hence in making observations with the thermometer for hypsometrical purposes, the instrument is not plunged into the water, but the whale instrument, bulb and stem, are by an apparatus used for the purpose plunged into the vapour arising from the boiling water. The degrees on the thermometer used are greatly enlarged, thus admitting of a minute subdivision of the scale and, consequently, of very precise readings. The following are a few of the barometric heights corresponding to different temperatures at which distilled water boils, taken from Regnault's tables revised by Moritz : - The temperature of the vapour of the boiling water being observed, the pressure is ascertained from the table, whence the height may be calculated, just as in the case of pressures obtained by means of a mercurial barometer.

The remark made by Sir John Leslie many years ago still holds good, that it is preposterous, in the actual state of physical science, to effect any high refinement in the formula for computing barometrical heights. What is required on the part of the computer of heights from barometrical observations is carefully to weigh the limits of error due to the instrument and methods of observations, to the hour of the day and the month of the year (see ATMOSPHERE, p. 28), and to the degree of unsettledness of the weather at the time the observations were made, and to give effect to these in the calculated results. From inattention to these simple considerations a large proportion of important heights given in works of travel and of physical geography are very erroneously stated, and consequently require careful revision.

For very rough approximations to the real height from observations of pressure and temperature, Sir G. B. Airy has prepared a table showing the differences of level corresponding to differences of pressure. It is from this table that the heights corresponding to pressures engraved on many aneroids are usually taken. The heights read off from the pressures should be corrected for observations of temperature carefully taken at the upper and lower stations, the mean of these two observations being assumed as the mean of the stratum of air occupying the interval between the two heights. (A. B.)