The formation of steam or aqueous vapour, and its diffusion in space or in a gaseous medium, have already been considered under the article Evaporation. We now propose first to take a view of various methods and devices which have been employed to detect the presence of aqueous vapour, and to ascertain its amount, or how much of it is contained in a given volume, whether when alone or diffused in a gaseous medium. This is necessarily connected with, and will in a great measure consist of, the description, theory, and use of such instruments as almost exclusively belong to this branch of inquiry, and which are usually denominated hygrometers, from ὑγρός, moist, and μέτρον, measure. We shall then consider under what circumstances moisture is deposited from the atmosphere, and shall examine some of the more remarkable phenomena resulting from or connected with the condensation of aqueous vapour.

Many contrivances bearing the name of hygrometers have appeared from time to time, and these, though extremely various in their constructions, we shall only divide into two very different classes: 1st, Such as are slow or uncertain in their indications, or are formed of decaying or changing materials; 2d, such as are not only more prompt in their indications, but are formed of materials comparatively free from change. The former are obviously unfit for hygrometers, but have been so numerous, that a description of the whole of them alone would greatly exceed our limits; which is the less to be regretted, since the greater and more superficial part have already served their day, and gone entirely into disuse. It will, however, be proper briefly to notice a few of those either already become obsolete, or soon to be so, were it only to show their imperfection.

The earliest account of hygrometers perhaps worth noticing is that contained in the Philosophical Transactions for 1676, where several are described, and allusions made to others; but both then, and during more than a century which followed, the indications of such instruments depended on the change which the weights or dimensions of bodies undergo from a change of humidity. Thus, when the weather becomes more damp, the deliquescent salts gradually become heavier from absorbing moisture, and in drier weather lighter from parting with it. The like happens with certain stones and various other minerals; with sulphuric acid and several other liquids; with sponges and many vegetable and animal substances, whose dimensions are considerably though slowly altered by change of humidity. In bodies of a fibrous structure, however, the change of dimension occurs principally in a transverse direction, or across the fibres, and but very slightly in the direction of their length. Thus a beam of straight-grained wood becomes thicker and broader by absorbing moisture, and vice versa; while its length is altered in a much smaller ratio. The same thing takes place with whalebone, ivory, and other substances.

As several sorts of wood are at first very susceptible of participating in the dryness and moisture of the atmosphere, they have sometimes been employed in the construction of hygrometers. For this purpose a small and very thin board is placed on edge, with its ends slightly entering into grooves in two upright pillars, its fibres being in a horizontal direction, so that the expansion or contraction of the board may be vertical; for, as was noticed above, it is principally in the lateral direction, or across the fibres, that wood expands or contracts by change of humidity. On the upper edge of the board is fixed an upright toothed rack, working in the leaves of a small pinion, on whose axis is fixed a wheel, which turns another pinion on the axis of the index. It is thus evident, that a very slight motion communicated to the rack, by the rising or falling of the upper edge of the board, will be greatly magnified by the wheel-work, so as to be shown in a very sensible manner by the index. But the defect of this and all similar contrivances is, that the wood takes such a long while to receive the impressions, whether of humidity or dryness, from the atmosphere, that by the time they indicate greater dampness, the air may have really become drier, and vice versa; and besides, the board gradually becomes less sensible to these impressions, till at length the index almost ceases to move.

An obvious consequence of the lateral expansion and contraction of organic fibres is, that ropes, cords, or strings, formed of such fibres twisted together, are rendered thicker and shorter by absorbing moisture, and vice versa. On this principle it has frequently been attempted to construct hygrometers, as, for instance, by making fast one end of a piece of rope, cord, or catgut, winding it backwards and forwards over several pulleys, and suspending from its other end a small weight, which, by rising and falling with the alternate shortening and lengthening of the cord, marks, on a graduated scale placed behind it, the changes of humidity. Sometimes the one extremity of the catgut being made fast, the other carries a small weight, and an intermediate part is wound on a small axis, carrying an index round a graduated plate, the degrees of which are meant to mark the humidity or dryness of the air. When a weight is suspended by a fine string, a piece of catgut, or the naturally twisted beard of the wild cat, it will be seen to turn in the one direction or the other, owing to the twisting and untwisting of the cord, from the changes of humidity. The hygrometer or weather-house, commonly sold as a toy, depends on this principle. It usually consists of a kind of box, representing a building with two doors, within which is suspended a horizontal bar, by means of a cord attached to its middle. Upon one end of this bar is a figure of a man, with an umbrella to protect him from the rain, and on the other that of a woman with a fan. They are so adjusted in respect of the doors, that when the man appears it is a sign of rain; but when he withdraws, and the woman presents herself, fair weather is predicted. This contrivance unfortunately has just the same faults as the one first noticed, being both liable to change and decay, so as ultimately to lose almost entirely its sensibility. It is therefore of no other use than as a mere toy; for the value of an instrument employed as a measure of any kind must depend not only on its being at first accurately constructed, but likewise upon its indications not being, ceteris paribus, liable to change.

The preceding remarks upon the effects of a change of humidity on organic substances may enable us to correct what we consider a great mistake. Slips of metal are sometimes employed to strengthen or bind together cabinet work; and this has been objected to on the professedly scientific ground, that the expansion and contraction of the metal by change of temperature is apt to tear, warp, or distort the wooden work. That some such effects as have just been stated do frequently occur, cannot be denied; but we have no hesitation in ascribing them to a very different and far more powerful cause, the lateral expansion and contraction of the wood itself by changes of humidity, and particularly the permanent contraction due to the gradual loss of natural sap, if the wood has not been Hygrometry—previously well seasoned; for the bad effects in question rarely appear at first, and only occur at all when the metal is of considerable length and fixed across the grain of the wood, and more especially when the wood has not been of the proper sort, or has been worked when damp or badly seasoned. Indeed, when a sufficiently strong slip of wood is firmly applied in place of and in the same position as the metal, there is, *ceteris paribus*, no sensible difference in the bad effects; and it is particularly to be remembered, that a rise of temperature which would alter the length of the metal so as to do any harm in the manner supposed, would seriously injure cabinet work although no metal were near it. Wood in general, if exposed to drought, continues to shrink permanently more or less, especially in the lateral direction, or across the fibres, so long as it lasts; and when alternately exposed to the expanding and contracting influences of moisture and drought, the permanent contraction is upon the whole accelerated and increased.

The hygrometer invented by the late ingenious Captain Kater depends upon the twining and untwining which the changes of humidity produce in the naturally twisted beard of grass known in the Canarese language by the name of *Oobeena Hooloo*. This is the *Andropogon contortum* of Linnaeus, and is gathered in the Mysore country in January. The frame of this instrument is commonly cylindrical; and, that it may allow the air to pass freely through, it is formed of small bars of brass, or sometimes of silver. Upon one end of this frame is soldered a flat plate, having a projecting rim, to protect the index which turns upon it over a circular dial divided into a hundred equal parts or degrees. The index, which is very slender and nicely balanced, is put on one end of an axis of silver wire, which has liberty both to turn round and to shift a little longitudinally through double conical holes in the frame. The axis extends about half the length of the frame; and a part of it next the index is formed into a screw of fourteen or fifteen threads. This is effected by twisting tightly round it a smaller silver wire. A loop and drop made of fine gold wire are so formed, that when suspended from the axis, the loop may slide freely along the screw, and by the number of threads thus run over, it can show the number of complete revolutions of the index. The farther end of the axis is swelled a little, and has a notch to receive the end of the *Oobeena Hooloo*, which is fixed by drawing upon it a sliding ring. This beard is then extended in the line of the continuation of the axis, till it meet the frame, where its other end is fixed similarly to the former one, but admits of adjustment by a screw which stretches it slightly. Such is a brief outline of the very simple and ingenious mechanism by which the gradual expansion or contraction of the hygrometric substance communicates a rotatory motion to the index; so that whilst the index shows the fraction of a revolution on the graduated dial, the loop and drop indicate the number of complete revolutions, or the integral number of hundreds of degrees which the index has passed over on the dial. So great is the sensibility of this instrument, that its index makes ten or twelve revolutions, while that of Saussure's only makes one. Captain Kater recommended that all observations made with his hygrometer should be reduced to what they would have been had the entire scale, or the utmost range traversed by the index, consisted of a thousand degrees, which would be ten complete revolutions. By this, we suppose, he meant to render all hygrometers of his construction comparable; a property which, however, belongs to no hygrometers whose principal parts are formed of animal or vegetable substances, which are continually changing, and gradually becoming less and less sensible to the influence of humidity.

Hygrometers have frequently been formed by suspending from one arm of a balance some substance which strongly attracts moisture from the atmosphere, and nicely counterpoising it by a weight on the other arm. The changes in the humidity of the air are then meant to be indicated by the changes in the position of the beam, arising from the gain or loss of weight in the suspended body. A great variety of substances have been used for this purpose, such as sponge, caustic potash, the deliquescent salts, sulphuric acid, &c. These, like the former instruments, are all too late in their indications, though some of them might scarcely be liable to lose their sensibility, were it not that they soon become useless from the accumulation of dust, soot, &c. especially if in or near a large city.

But the expansions and contractions of hair and of whalebone are, from the tenacity of their substance, somewhat more expeditious in acquiring the humidity or dryness of the surrounding air. They have therefore been employed in the construction of hygrometers; the former by Saussure, and the latter by Deluc. Both these instruments are impaired by time, and they sometimes acquire contrary errors. Their indications generally differ materially, even when graduated alike, and more especially when differently graduated; but so unsteady is the relation between them, even for the same state of the air, that no certain rule can be given for reducing the one to the other. This is evident from the circumstance, that scarcely two authors who do not derive their information from the same source agree respecting the relation between the indications of these instruments. Deluc states, we think, very just objections to Saussure's hygrometer, and as justly does Saussure object to his; so that, had it not been out of respect for the high reputation of these philosophers, and the frequent reference made to their instruments in scientific researches, and in books of voyages and travels, we should scarcely have felt warranted to give even the following brief description of them here. We begin with that of Saussure, which is represented in fig. 3, Plate CCXCV.

The lower end of the hair *ab* is held by the screw-pincers *a* at the bottom of the frame. These pincers, shown separately at B, fig. 4, terminate in a screw which enters the hollow screw C, fig. 5. By turning this screw, the pincers *b* or B may be raised or lowered at pleasure. The other end *a* of the hair is held by the inferior mouth of the double and moveable pincers *a*, seen separately at A, fig. 6, and which, with their upper mouth, take hold of a fine well-tempered silver wire, which is wound round the arbor *d*. This arbor, seen separately at DF, fig. 6, carries the index *ee*, marked E in the separate figure 6, and is cut like a screw, with a flat-bottomed groove to receive the silver wire, which, as mentioned above, is connected with the hair by means of the double pincers. The wire was adopted from its being found that, when the hair itself was wound on the arbor, it became rough, and contracted a stiffness, which the small weight *g* or G, employed as a counterpoise, could not overcome; whereas a proper wire always preserves the same flexibility. It was necessary thus to cut the arbor like a screw, that the wire might not have its coils wound one upon another, so as to thicken the arbor, or to take a position too oblique and uncertain. The wire is fixed to the arbor by a small pin F. The other end D of the arbor has the form of a pulley, with a groove flat at the bottom to receive a fine silk thread, by which is suspended the counterpoise marked *g* in fig. 3, and G in fig. 6. This is intended to keep the hair always gently stretched. One end of the arbor, formed into a fine pivot, passes through the centre of the dial, and carries the index *ee* on its extremity. The other end has a similar pivot turning in the arm *h* of the doubly-kneed piece *hi*, or HI, fig. 7, which is fixed to the back of the dial *hh* by the screw I. The dial is divided into 360 degrees, and is soldered to two tubes *ll*, which surround and can be slid up and down the two upright wires. The dial can thus be fixed at any place on the wires by means of the screws \( mn \). The square column \( pp \) carries a box \( q \), to which is fixed a sort of pencil-case \( r \), fitted to receive the counterpoise \( g \). When the hygrometer is to be transported to another place, and some harm is apprehended from the vibrations of the counterpoise, the case \( r \) is raised to receive it. Both are then made fast by the screws \( s \) and \( t \). When, again, the hygrometer is to be used, the counterpoise is disengaged, and the box lowered as in the figure. At the corners of the base of the frame are four screws \( o, o, o, o \), for the purpose of levelling the base, or making the instrument stand upright. The three columns of the frame are connected at the top by the crooked piece \( yzy \), having a hole at \( y \), by which the instrument may be suspended.

The point of extreme dryness is obtained by placing the instrument under a receiver, with a quantity of quicklime or caustic alkali; and that of extreme moisture by enclosing it in a receiver whose sides are kept continually moistened. This last Deluc regards as very fallacious.

The scale of Saussure's hygrometer sometimes contains 100 divisions or degrees, and sometimes a larger number. That in our figure has 360. Saussure gives a decided preference to human hair, which he first causes to undergo a preparation, for the purpose of divesting it of a kind of natural oiliness, which, if not removed, would render it less sensible to the action of humidity. This preparation is made at the same time on a considerable number of hairs forming a tuft, the thickness of which need not exceed that of a quill. This tuft being enveloped in a bit of fine cloth, as in a case, is immersed in a long-necked phial full of water, holding in solution about the hundredth part of its weight of sulphate of soda, and which is made to boil about three minutes. The tuft is then passed through two vessels of pure water at the boiling temperature; afterwards the hairs are drawn from their wrapper and separated; then they are hung up to dry. It only remains to select those which are cleanest, softest, most brilliant, and most transparent. The effects of dryness and of moisture upon the hair are modified by those of heat, which affect it in different ways. Thus, if it be supposed, for example, that the air becomes warmer about the hygrometer, its drying quality being thereby increased, it will abstract from the hair a part of the water which it had imbibed, thus tending to shorten it; while, on the other hand, the heat, by expanding the hair, will tend, though in a much smaller degree, to lengthen it; so that the total effect will consist of the excess of the former over the latter. It is therefore necessary, where precision is aimed at, to consult the thermometer, and apply a corresponding correction.

In his *Essais sur l'Hygrométrie*, M. de Saussure, while candidly acknowledges the imperfection of his own instrument, enumerates the following as properties which he thinks a perfect hygrometer ought to possess: 1st, Its variations should be sufficiently extensive to show very small changes of humidity or dryness; 2d, these indications should be so prompt as to proceed *pari passu* with the actual state of the air; 3d, the instrument should always accord with itself; that is to say, in the same state of the air it should always be found at the same degree; 4th, it should be comparable; that is to say, any number of hygrometers constructed separately upon the same principles should always indicate the same degree in the same circumstances; 5th, it should only be affected by humidity or dryness properly so called; 6th, the variations in the indications should be proportional to those of the air; so that, in like circumstances, a double or triple number of degrees should always indicate a double or triple quantity of moisture.

This last property, however, we cannot regard as by any means indispensable to a perfect hygrometer, though we grant that an instrument possessing it is likely to be somewhat more convenient. For it is quite clear, that if we only knew the true relation between the indications of the instrument and the state of the air, we could by that means compute the degree of humidity with perfect certainty; no matter how much the variations of the indications of the instrument and those of humidity differed from simple proportionality.

We shall next give a brief description of Deluc's hygrometer. The frame will be readily understood from inspecting fig. 1, Plate CCXCV. The principal part consists of a slip of whalebone, cut transversely, or across the fibres, and is represented by \( ab \). Its end \( a \) is held by a very simple sort of pincers, made of a bit of flattened wire bent and pressed together on the whalebone by a sliding ring. The other end \( b \) is fixed to a bar \( c \), which can be moved by a screw for adjusting the index \( e \), to have a proper position at first on the dial. The loop of the pincers which hold the whalebone is hooked to the end of a thin brass wire, to the other end of which is also hooked a very thin silver gilt lamina, which has at that extremity pincers similar to those of the whalebone; but its other extremity is pinned into a hole in the axis. The spring \( d \) which stretches the whalebone is made of silver gilt wire; it exerts a force equal to a weight of twelve grains, but with this among other advantages over a weight, that in proportion as the slip is weakened by lengthening, the spring relaxes its force by unbending. The axis has very small pivots, whose ends are confined, to prevent the shoulders from rubbing against the frame. A section of this axis is shown on a large scale in fig. 2. The slip acts on the diameter \( aa \), and the spring on the smaller diameter \( bb \). The point of extreme dryness is obtained by enclosing the instrument under a receiver, along with some quicklime; that of extreme humidity, by wetting the whalebone with water, or immersing the whole instrument in it. The graduated arc on the dial is about five sixths of the entire circle, and is divided into 100 equal parts or degrees. The zero denotes extreme dryness, and the 100th degree extreme humidity. Saussure, however, alleges that the whalebone is more thoroughly soaked or swelled by immersion in water than in the most humid air, which, he says, never brings it to the extremity of the scale.

Deluc maintains that hairs and other animal or vegetable hygroscopic substances taken lengthwise, or in the direction of their fibres, undergo contrary changes from different variations of humidity; that when immersed in water, they lengthen first, and then shorten; that when they are near the extreme of humidity, they shorten with an increase and lengthen with a diminution of humidity. This he regards as the necessary consequence of their organic reticular structure; and in illustration of it he has given the following comparison between the corresponding indications of his own hygrometer and those of Saussure. The scale of each is supposed to be divided into 100 degrees.

| Deluc | Saussure | Deluc | Saussure | |-------|----------|-------|----------| | 5 | 15-6 | 55 | 88-8 | | 10 | 29-4 | 60 | 91-6 | | 15 | 40-9 | 65 | 93-8 | | 20 | 50-5 | 70 | 95-6 | | 25 | 59-2 | 75 | 97-2 | | 30 | 68-8 | 80 | 98-0 | | 35 | 73-0 | 85 | 100 | | 40 | 78-3 | 90 | 100 | | 45 | 82-1 | 95 | 99-3 | | 50 | 86-1 | 100 | 98-3 |

VOL. XII. Hygrometry.

From this it would appear, that after the hair becomes very moist, its lateral expansion produces a contraction in the length, as in the case of ropes. Saussure, however, alleges that in this trial his instrument must have been in bad order; and he even retaliates by ascribing as great defects to that of Deluc. According to Boeckman, 10, 20, 30, 40, 45 of Deluc correspond to 33, 54, 65, 80, 86 respectively of Saussure; but in atmospherical observations he found Deluc's at 56 and 48, when Saussure's indicated 85 and 90 respectively.

M. Guy-Lussac has made many experiments on the hair hygrometer, which would place it in a rather more favourable light than the above; and M. Biot has exerted his great analytical skill in endeavouring to perfect its theory, by giving, in his Traité de Physique (tome ii. p. 199), a very elaborate investigation of the relation between its indications and the actual humidity, which has been further illustrated at great length by Signor Melloni, in the Annales de Chimie et de Physique for January 1830. But unfortunately this relation is so soon deranged by the rapidly changing and perishable nature of the instrument, as to render all such labours of very little use, no matter how much learning or ingenuity may have been expended on them.

It will be unnecessary here to notice Deluc's ivory hygrometer, because a description of an improved instrument of the same kind will be found under the article Meteorology.

Mr Wilson's hygrometer is very similar to a mercurial thermometer; but in place of the bulb being of glass, it consists of a rat's bladder, which when new is very sensible to changes of humidity; so that by expanding with moisture, or contracting with drought, it produces corresponding depressions, or rises in the column of mercury in the glass stem. This instrument must obviously have its indications somewhat affected by changes of temperature like a thermometer; and, in addition to some of the imperfections common to the instruments already described, it has been objected that the pressure of the column of mercury in the stem must occasion a variable, and perhaps increasing distension of the bladder.

The foregoing we presume to be sufficient specimens of such hygrometers as are slow or uncertain in their indications, or formed of comparatively changing and perishable materials. These, too, we should think, have been treated at as great length as the little and decreasing importance now attached to them seems to warrant. But since the science of heat lies at the foundation of all accurate knowledge in hygrometry, we now propose, preparatory to entering on the consideration of such hygrometers as are more durable in their construction and constant in their indications, to investigate some relations of air to heat, which will be useful in the sequel of this article. In so doing we shall reason from admitted principles only; for we see no necessity for calling in the aid of the old notion which some are so anxious to revive again, that heat is a species of motion; because such a hypothesis, in place of solving the difficulties, is, like "the occult qualities," a mere subterfuge for our ignorance, or an excuse for not encountering the difficulties, and unavoidably leads to still greater difficulties; whereas the more closely the other theory is traced, the more the difficulties, numerous as they still are, disappear. Of this we shall have occasion to notice several instances in the course of this research. We now begin the investigation with a brief demonstration of the following preliminary proposition.

Lemma.—If the area of a curve between every two ordinates be such that, when cut by a third ordinate in a given ratio, the two corresponding differences in the logarithms of the three abscissae are likewise in that ratio, the curve is a hyperbola.

Let the curve ABC be such, that when AHKC, its Hygro area between any two ordinates AH, CK, is cut by any third ordinate BI, making area AHKC to AHIB in the given ratio of m to n, the three corresponding abscissae reckoned on the straight line GH from a fixed point G, are related thus: log. GK — log. GH : log. GI — log. GH :: m : n, the curve ABC is a hyperbola.

For if not, with G as a centre, GH as one asymptote and the other parallel to AH, describe through B the hyperbola aBe cutting AH and CK in a and c. Then by the well-known property of the hyperbola,

area aHKc : aHIB :: log. GK — log. GH : log. GI — log. GH.

But AHKC : AHIB :: log. GK — log. GH : log. GI — log. GH;

therefore, by equality of ratios, alternation and division,

BIKC : BIKe :: AHIB : aHIB.

If eK < CK, and aH > AH, and if the curves do not again meet between A and C, the first term of the analogy last stated must exceed the second, while yet the third is less than the fourth, which is absurd. The like would as readily follow, were eK > CK and aH < AH.

But it is evident that in every case in which the hyperbola is supposed to cut the other curve, the same process of reasoning will lead to the like absurdity, if three ordinates intercepting areas in the given ratio be drawn so close together as to embrace no other meeting of the curves but the foresaid intersection. Now such a construction is always practicable; for in every case two of three such ordinates may be drawn arbitrarily, viz. one through the point of intersection, and a second as close as we please to either side of it; whilst the abscissa which gives the position of a third still nearer, if wished, on the other side, may be had from such an analogy as was stated above, namely,

log. GK — log. GH : log. GI — log. GH :: m : n.

It is indeed a supposable case, that the hyperbola, in place of cutting, might have the other curve wholly on one side, only touching it in the point B; but then it is evident that another hyperbola drawn near enough to that side of the former one, and having the same asymptotes, could not fail to cut the curve ABC. Of course, three ordinates being drawn as before, viz. one through the point of intersection, and the other two near enough to it, would still produce the former absurdity. Hence the curve ABC can only be a hyperbola.

The physical principles which we are about to employ as data for investigating the relations of air to heat, are essentially the same as those from which MM. de Laplace and Poisson attempted to deduce the true scale of the air-thermometer, as may be seen in the Mécanique Céleste (tome v. p. 127), and Annales de Chimie et de Physique (tome xxiii. p. 337); where, after proceeding so far, and with data which, if properly managed, were amply sufficient for their purpose, they abandoned the project, and contented themselves with assuming that the common mode of graduating an air-thermometer forms a true scale of temperature. This they were forced to do in consequence of having adopted a mode of investigation so unnecessarily abstruse that it soon became quite unmanageable. That they should have failed to prove the common scale to be the true one, need excite no surprise; for we shall soon see that such a result would be quite incompatible with the very principles from which they attempted to deduce it, and that, without the aid of any assumption, a much more simple process of reasoning, illustrated by a diagram or two, would have necessarily led them to the legitimate, though a very different, result. These principles or data, and some inferences from them, we shall now distinctly state, numbering a few of the paragraphs as we proceed, chiefly for the sake of after reference, and not as if we were specifying so many independent data; for the whole force of the reasoning rests on the first two; the third is merely an inference from the second; and the only use here made of the fourth and fifth is to trace more readily, in known terms, the relation between the common scale of the air-thermometer and the results to which this investigation leads.

1. The law of Boyle and Mariotte, that at the same temperature the elasticity or pressure of air is as its density, or inversely as its volume; and consequently, while air undergoes the same change of temperature, its volume varies under a constant pressure, precisely in the same proportion as the pressure would do were the air confined in an inextensible vessel.

2. If \( s \) denote the specific heat of air when it sustains a constant pressure, and \( s' \) the specific heat of the same mass of air when confined in an inextensible vessel; then it has been ascertained, through a great range of temperature and pressure, as will be afterwards explained, that \( s \) always exceeds \( s' \) in a constant ratio, which we may now call the ratio of \( m \) to \( n \), which are constants; but their values not being now given, will show our investigation to be independent of the value of their ratio.

These two, viz. the law of Boyle and the constancy in the ratio of \( m \) to \( n \), are the principles to which we have alluded above as being employed by MM. de Laplace and Poisson, and as being quite sufficient, if properly managed, to have unavoidably led these great mathematicians to the conclusion that air expands in geometrical progression for equal increments of heat. But this, and most of the other legitimate results, they failed to reach, in consequence of unnecessary intricacy, and their introducing an assumption which we shall shortly see to be quite incompatible with the data now specified. The second principle, as will be afterwards noticed more particularly, was first shown by the illustrious M. de Laplace himself to be a necessary deduction from the fact ascertained by the experiments of MM. Desormes and Clement, and more especially by those of MM. Gay-Lussac and Welter, which were continued through a great range of temperature and pressure, viz. that when the density of air suffers a minute and sudden change, \( m \) times such variation of density is to the whole density as \( n \) times the accompanying variation of pressure to the whole pressure. Or, \( \varepsilon \) being the density and \( p \) the pressure,

\[ \frac{mdp}{p} = \frac{mdp}{p'}; \quad \text{and} \quad \frac{mdp}{p} = \frac{mdp}{p'}. \]

3. The last equation evidently expresses the relation between the fluxions of the logarithms of the pressure and density of air when the total heat in it is constant. The fluent is \( n \log_p p = m \log_\varepsilon \varepsilon + C \); so that if \( p' \) and \( \varepsilon' \) be put for the initial values of \( p \) and \( \varepsilon \), we have \( C = n \log_p p' - m \log_\varepsilon \varepsilon' \); and

\[ n \log_p \frac{p}{p'} = m \log_\varepsilon \frac{\varepsilon}{\varepsilon'}; \quad \text{or} \quad \left( \frac{p}{p'} \right)^n = \left( \frac{\varepsilon}{\varepsilon'} \right)^m, \]

which is the relation between the pressure and density of air, when the total heat in it is invariable.

4. It has been ascertained by Dr Dalton, M. Gay-Lussac, &c. that on heating air under a constant pressure from \( 32^\circ \) F. to \( 212^\circ \), its bulk acquires an increase of three eighths. Such increase, in the common graduation of the air-thermometer, is divided into 180 equal parts or degrees for Fahrenheit's scale; and the like divisions corresponding to equal variations of bulk, are continued both above \( 212^\circ \) and below \( 32^\circ \), viz. upward indefinitely, but downward they have a limit; for as three eighths are to \( 180^\circ \), so is the whole bulk at the freezing point to \( 480^\circ \); and therefore more than 480 degrees cannot with propriety be reckoned or put below \( 32^\circ \) on the Fahrenheit scale of an air-thermometer.

5. Since the freezing point is marked \( 32^\circ \), it is obvious that 480 degrees will reach from it down to \( -448^\circ \). The bulk of a given mass of air, therefore, under a constant pressure, varies as its temperature reckoned from \( -448^\circ \) on the common scale; that is, as \( t + 448 \), the degrees of Fahrenheit being \( t \). Hence, by art. 1, the pressure of air confined in an inextensible vessel, likewise varies as \( t + 448 \).

We shall now apply these principles to determine the scale of temperature for air. Let ABC be a curve, such that, while AHIB, its area between any two ordinates, denotes an addition to the heat contained in a given mass of air, the straight line HI shows on the common scale the consequent rise of temperature, under a constant pressure, viz. from H to I, as indicated on the common scale of an air thermometer. Let DEP be a similar curve, making \( AH : DH :: m : n \), and cutting all the other ordinates and areas of ABC in that same ratio. Hence, area DHIE is equal to \( \frac{n}{m} (AHIB) \), and it therefore (art. 2) represents the smaller addition of heat which would be sufficient to raise the temperature of the same air from H to I, were that air, in place of being free to expand under a constant pressure, confined in an inextensible vessel. For since the specific heats or the minute increments are always in the ratio of \( m \) to \( n \), so must any larger addition of heat raising the temperature from H to I under a constant pressure, be to that producing the same rise under a constant volume. Let the common scale, of which HI is a part, be continued downward to the point G answering to \( -448^\circ \) Fahrenheit; then (art. 5) the volume of the air is increased, under a constant pressure, in the ratio of GI to GH, by its temperature being raised from H to I. Suppose, therefore, that the air, after having, under a constant pressure, received an increase in its total heat equal to AHIB, and thereby acquired the temperature I, is instantly compressed to its original volume; by which means its temperature is suddenly raised from I to K on the common scale, in such a manner that area DHKF = AHIB; because the air is evidently now raised to the same temperature, and in every respect brought to the same state as if, with its original volume all the while invariable, it had received the same increase in its quantity of heat as is mentioned above, and which is now denoted by area DHKF instead of AHIB.

While the air was thus being compressed to its original volume, or the density re-increased in the ratio of GI to GH, the pressure has been thereby increased (art. 1) in the same ratio compounded (art. 5) with the ratio of GK to GI for the second rise of temperature; that is, in the ratio of GK to GH; and during this compression the total quantity of heat in the air is supposed to be constant. Hence,

\[ \text{(art. 3)} \quad \frac{GK}{GH} = \frac{p}{p'}, \quad \frac{GI}{GH} = \frac{\varepsilon}{\varepsilon'}, \quad n \log_p \frac{GK}{GH} = m \log_\varepsilon \frac{GI}{GH}. \] Hygrometry.

Hygrome- and therefore log. GK — log. GH : log. GI — log. GH :: m : n. But we have also area AHKC : AHIB :: m : n, because AHIB = DHKF; and the same thing holds at any part of the curves. Consequently, by the lemma, each of these curves is a hyperbola, having G' for its centre and GH for an asymptote.

All the preceding reasoning evidently applies as well to the accented letters in the lower part of the figure, where AHIB', the area between any two ordinates, denotes a loss of heat, HI' the consequent depression of temperature on the common scale in cooling from H to I' under a constant pressure, and IK' a farther depression, such that area DHKF' = AHIB'; being caused by suddenly dilating, to its original volume, the air which had just been contracted by cooling from H to I'.

Since in each curve the segments of the area denote variations of heat, while the corresponding segments of the abscissae denote variations of temperature on the common scale, it follows from the known property of the hyperbola, that while the variations of the quantity of heat in air under a constant pressure are uniform, those on the common scale of an air-thermometer form a geometrical progression. Or, in more general terms, while the variations in the quantity of heat in air are uniform, the variations of its volume, under a constant pressure, form a geometrical progression, as do likewise the variations of pressure under a constant volume.

Hence, in place of being equal, the divisions on a true scale of an air-thermometer should form a geometrical progression, increasing upward, such that the length of each division may be proportional to its distance from — 448° F.; and hence also the values of the degrees usually put on Fahrenheit's scale of an air-thermometer decrease upward, the value of each being inversely as its distance from — 448°. The same thing holds regarding any other scale with equal divisions.

Such are some of the necessary results of the very principles from which MM. de Laplace and Poisson failed to deduce a corresponding scale of temperature; we mean a scale which should necessarily follow from, and be compatible with, the law of Boyle and the foresaid constancy in the ratio of m to n. But having failed in this, they attempted to supply the defect, by assuming that the variations in the quantity of heat in air, under a constant pressure, are proportional to the corresponding variations on the common scale of an air-thermometer. We shall merely notice so much of their investigation here as will be sufficient to show the utter incompatibility of such an assumption with the two principles just named. These illustrious philosophers set out with an equation which, adapted to Fahrenheit's scale, is

\[ p = a \left( t + 448 \right) \]

To this we have no objection. It just expresses the relation between the law of Boyle and the common scale; \( p \) being the pressure, \( g \) the density, and \( t \) the temperature, of a given mass of air; also \( a \) is a constant and \( r \) a given temperature on Fahrenheit's scale. Having next introduced the assumption in question, they obtain the equation,

\[ q = A + B(t + 448)p^{\frac{m}{n}} \]

where \( q \) is the quantity of heat to be added or withdrawn, in order to change the temperature of the given mass of air from \( r \) to \( t \); \( A \) and \( B \) are constants, and \( m \) and \( n \) numbers in the constant ratio already defined. By combining the two equations, we have likewise

\[ q = A + B(r + 448)p^{\frac{m}{n}} \]

Taking the fluxion of this with the density \( g \) constant, we have \( dq \) varying, as \( p^{\frac{m}{n} - 1} dp \). But the constancy in the ratio of \( m \) to \( n \) provides that the change to be made in the quantity of heat in air, in order to produce a given change in its temperature, under a constant pressure, must be proportional to the change of heat necessary to produce the same change of temperature, were the volume constant; and it is well known to be the same thing, whether variations of temperature on the common scale are reckoned by the variations of volume under a constant pressure, or by variations of pressure under a constant volume. Hence Laplace and Poisson assume the variations in the quantity of heat to be proportional, as well to the variations of pressure under a constant volume, as to the variations of volume under a constant pressure. Therefore \( dq \) varies as \( dp \) simply; but we have just seen that it likewise varies as \( p^{\frac{m}{n} - 1} dp \). Consequently \( p^{\frac{m}{n} - 1} dp \) varies as \( dp \); and dividing by \( dp \), we have \( p^{\frac{m}{n} - 1} \) varying as a constant quantity, which is extremely absurd. Yet the very same data and assumption which give rise to this contradiction, form the foundation of many intricate formulæ in the Mécanique Céleste, and of a very long memoir on heat by M. Poisson, in the eighth volume of the Mémoires de l'Académie.

From the remarkable inconsistency just pointed out in the principles adopted by these illustrious philosophers, it is evident that they had not had so much as a conjecture of what the legitimate result should be. Nobody wonders when a research of this sort fails in the hands of an inexperienced tyro; but if those who are deservedly regarded as at the head of their profession be liable to deceive themselves in so remarkable a manner, how cautious ought we to be in receiving even what emanates from high authority, if accompanied by nothing deserving the name of argument or intelligible evidence; for the foregoing investigation, we presume, will be found to be both legitimate, and to depend on nothing but admitted principles. It is long since our distinguished countryman, Dr Dalton, proposed what he alleged to be the true scale of the mercurial thermometer, founded on the supposition that the expansions of liquids were everywhere as the squares of their true temperatures, setting out from the greatest density of each. With this he coupled another speculation: he supposed that, relatively to equal intervals on his new scale of temperature, the expansions of air, or of any other gas, under a constant pressure, formed a geometrical progression; which evidently was a very different scale from the one we have deduced above, because, as will presently be seen, it bore such a different relation to the expansion of mercury. For, unfortunately, these views, which Dr Dalton had never shown to be necessarily deducible from admitted principles, were soon found to be mutually incompatible; but of the two hypotheses, that regarding the expansion of mercury being the greater favourite with Dr Dalton, he rather chose to retain it, and abandon the one respecting the expansion of air; in place of which, he has since, in his Chemical Philosophy (vol. ii. p. 298, published in 1827), adopted the very different notion, that it is the forces of steam, and of other vapours in the state of saturation, which form geometrical progressions for equal intervals of temperature. It was absolutely necessary that the one of his former hypotheses should be relinquished; for they were not only inconsistent at extreme temperatures, but they required the common mercurial thermometer to be more than 7° below the common air-thermometer at 122° F.; whereas at that point, several eminent French chemists declared they could find no such difference; and in their decision Dr Dalton at length acquiesced. However, from the recent comparison of these two instruments by Dr Prout, it appears that their indications do not everywhere coincide throughout the interval between the freezing and boiling points of water; but their difference is quite of the contrary sort to that which Dr Dalton alleged, the mercurial thermometer being in advance of the other.

It was shown (art. 3) that \( \left( \frac{P}{P'} \right)^n = \left( \frac{\varepsilon}{\varepsilon'} \right)^m \); viz. that when the total quantity of heat in a given mass of air is constant, the \( n \)th power of the pressure varies as the \( m \)th power of the density; and since \( m \) is greater than \( n \), the pressure varies faster than the density, or \( \frac{P}{P'} = \left( \frac{\varepsilon}{\varepsilon'} \right)^m \). But in this, a part of the variation of pressure is due to change of temperature; for (art. 1) when the temperature is the same, the pressure and density vary in the same ratio. Also (by art. 1 and 5), when along with a change of density from \( \varepsilon \) to \( \varepsilon' \), the temperature changes from \( t \) to \( t' \), and the pressure from \( P \) to \( P' \), they are related thus; \( \frac{P}{P'} = \left( \frac{\varepsilon}{\varepsilon'} \right)^m \).

\[ \frac{t + 448}{\tau + 448} = \left( \frac{\varepsilon}{\varepsilon'} \right)^m = \left( \frac{P}{P'} \right)^m; \]

and therefore, on the common scale, the change of temperature is

\[ t - \tau = (\tau + 448) \left[ \left( \frac{\varepsilon}{\varepsilon'} \right)^m - 1 \right] \]

\[ = (\tau + 448) \left[ \left( \frac{P}{P'} \right)^m - 1 \right]; \]

when the total quantity of heat in the air is constant. This investigation is given in general terms, but we shall soon see that \( m \) is to \( n \) either exactly or very nearly as 4 to 3; and therefore,

\[ \frac{m - n}{n} = \frac{1}{3}, \quad \frac{m - n}{m} = \frac{1}{2}. \]

Most of the formulae which have been proposed for this purpose are fraught with inconsistencies, such as making the rise of temperature which would be produced by a quadruple compression, to be very different from the sum of the separate rises which should be produced by twice doubling the density; and they are equally faulty when we compare a quadruple dilatation with twice halving the density. Nay, when we attempt to retrace our steps by reversing either process, they do not restore the air to the same temperature and pressure which it had at first; but the formulae now given, unless when sadly mismanaged, lead to no such inconsistencies. Thus, suppose the density of air at the temperature of 60° to be quadrupled, the rise of temperature is (60 + 448)

\[ \left[ \left( \frac{4}{1} \right)^3 - 1 \right] = 298°4. \]

To effect the same thing by two separate doublings, we have first 508 \[ \left[ \left( \frac{2}{1} \right)^3 - 1 \right] = 132°04, \]

which, added to the initial temperature 60°, makes 192°04; and by doubling again the density of the air at this higher temperature, the second rise is (192°04 + 448) \[ \left[ \left( \frac{2}{1} \right)^3 - 1 \right] = 166°36. \]

So that the total rise is 132°04 + 166°36 = 298°4, the same as before. The like consistency will be found to hold with any proper trial of these formulae.

(See Edinburgh Phil. Journ. for July 1827, p. 153.)

From the foregoing investigation it is likewise evident, Quantity that if the total heat in a given mass of air undergo no change, while its density is being increased in any assigned ratio, as, for instance, in the ratio of GI to GH (see the preceding figure), the temperature is thereby raised from volume I to K on the common scale, making area DHKF = AHIB. In this case the area EIKF = ADEB represents the heat which has been elicited from a latent state, or rendered sensible by the compression. But if, on the contrary, the density of the air were diminished in the ratio of GI' to GH, without any change in the quantity of heat, the temperature would be thereby lowered from I' to K', making area DHKF' = AHIB'; and area EIKF' = ADEB' would denote the heat absorbed by the dilatation, or rendered latent without being actually lost. Now,

area EIKF = \( \frac{m - n}{n} \) (DHIE) = \( \frac{m - n}{n} \) (DHKF), and

EIKF' = \( \frac{m - n}{n} \) (DHI'E') = \( \frac{m - n}{n} \) (DHKF'); where-

fore area EIKF, or the heat evolved by compression, bears the same ratio to DHIE that the \( \frac{m - n}{n} \) part of the increase in the logarithm of the density bears to log. GI — log. GH; and the same is also the ratio which area EIKF', or the heat absorbed by the dilatation, bears to DHIE', or which the \( \frac{m - n}{n} \) part of the decrease in the logarithm of the density bears to log. GI' — log. GH. In both cases, the \( \frac{m - n}{n} \) part, or one third of the change in the logarithm of the density, is equal to the \( \frac{m - n}{n} \) part, or one fourth of the change in the logarithm of the pressure; the total heat remaining invariable. It matters not what sort of logarithms are used.

Although the constancy in the ratio of the specific heats, Specific or of \( m \) to \( n \), as already defined, had been well ascertained by the experiments of Gay-Lussac and Welter, and been likewise adopted as a fundamental principle by the leading philosophers both here and on the Continent; yet the most important of its necessary and unavoidable consequences were long overlooked, especially how very different a gradation of the intensity of its pressure if constant, and the intensity of its pressure if constant.

A more obvious consequence likewise noticed in that paper, and of importance here, is, that the specific heat of the same mass of air under a constant pressure, must be independent of the intensity of such pressure; and that when the same mass of air is confined in an inextensible vessel, its specific heat must be independent of the size of that vessel. This admits of the most rigorous demonstration, and might even have been inferred from the consideration that the above-mentioned constancy in the ratio of the specific heats keeps the quantity of heat, which merely raises the temperature quite distinct from what is absorbed, or goes to enlarge the volume, and which is represented by the area between the two curves in the last figure. Now the remarkable curiosity is, that in the Mécanique Céleste, livre xii. chap. 3, formulae professedly derived from the same data are given for expressing the different values which the specific heat is fancied to have under different constant pressures, and also its supposed different values under different constant volumes. The same are given by M. Poisson (Annales de Chimie, xxiii. 338). M. Laplace had previously given in that journal (xviii. 185) a very different, though still a variable value to the specific heat of air; but this he virtually discarded, by subsequently adopting the other, though both are alike incompatible with the principles from which they profess to be deduced. Sanctioned by such names, these formulae are and must be received as orthodox by those who never think for themselves, or who do not thoroughly examine the investigations by which such expressions are deduced. But since the clearing up of this point is of great importance in researches of this nature, we shall endeavour to put the matter beyond dispute, by giving, from the very data used by Laplace and Poisson, a very simple demonstration of what we have now alleged, and which is the more satisfactory as it does not require the law of temperature to be previously decided upon; for since the same degree may be used for the several specific heats, it may be supposed to belong to any scale.

Let therefore the temperature of a given mass of air be reckoned on any scale of which the straight line BE is a part; and let CF be a line, no matter to our present purpose whether straight or curved, if it be such that every two ordinates may, like BC and EF, intercept an area BCFE proportional to the quantity of heat which would raise the temperature of the mass of air, under a constant volume, from any point B in the scale to any other point E in it. Let DG be a similar line or curve, so as to make the area BDGE proportional to the heat which would raise the temperature of the same mass, if under a constant pressure, from B to E. Now the chief condition on which we proceed is, that the quantities of heat represented by every two areas, such as BDGE and BCFE, between the same parallels, may be to each other in the given ratio of m to n, and which is obviously the same with the ratio of any ordinate of DG to the corresponding ordinate of CF. Let the point B mark the initial temperature, whatever that may be, of the given mass of air; raise this temperature from B to any other point E under a constant pressure; make Es one degree, draw the ordinate efg. Then area EGge is the specific heat, at the temperature E, of the same mass of air dilated by heat under the original pressure remaining constant. Now the specific heat, when the pressure is constant, is always to the specific heat when the volume is constant as m : n; but area EGge : EFe : : m : n; therefore EFe would be the specific heat at the temperature E, under the dilated volume, were it made constant. But since area BCFE is the quantity of heat which would raise the temperature from B to E under the original volume, and area EFe the heat which would raise it one degree more; therefore EFe would still have been the specific heat of the same mass of air at the temperature E, and all the while under the original volume. Hence EFe is the specific heat of the same mass of air at the temperature E, whether under the dilated volume remaining constant, or under the original volume constant.

Again, suppose the air to be heated up from B to E under the original volume remaining constant, by which means the pressure will be gradually augmented; but by the data, the specific heat at the temperature E, under the augmented pressure, were that now made constant, must exceed EFe in the ratio of m to n; wherefore EGge, which exceeds EFe in that ratio, is the specific heat of the same mass of air at the temperature E, whether under the augmented pressure remaining constant, or, as in the first case above mentioned, under the original pressure constant. The same conclusions would obviously follow by a similar process of reasoning, taking the second temperature at any point E' lower than B. Both cases might also be proved in several ways, a little differently from the preceding; as, for instance, by showing that EFe or EFe' jFe will be the specific heat of the same mass of air under a constant volume, as well after the temperature has been changed from B to E or E' by a change in the quantity of heat only, as by a change in the volume only; and of course EGge or EGge' will be the corresponding specific heat under a constant pressure, whether under the original pressure constant, or under the pressure made constant after being thus changed.

It is thus clearly established as a necessary result of admitting the constancy of the ratio above mentioned, that neither the magnitude of a constant volume, nor the intensity of a constant pressure, has any thing to do with the specific heat of a given mass of air. From this it is obvious that the specific heat of a given volume of air is, ceteris paribus, as its mass or density.

The experiments of Desormes and Clement on the specific heats of gases (Journal de Physique for December 1819), have been supposed to make the specific heat of a given volume of air to vary as the square root of its density; but we do not see how they warrant any thing of the sort. These distinguished chemists having enclosed air in a glass globe, placed it in an empty trough, which they next filled up with hot water, and assumed that the specific heat of the air was exactly proportional to the time which it and the globe took to acquire the same temperature with the water; whereas, for ought that is known to the contrary, the specific heat of the air might follow some other power or root, or some very complex function of the time. Nor do they make any allowance for the share which the mass or matter of this globe, which far exceeded that of the included air, had in protracting the time; or for the different mobilities, and consequently different conducting powers, of different gases, or of the same gas at different pressures. Thus, when the globe was filled with hydrogen, it was probably from the extreme mobility and great conducting power of that gas that the time of its attaining the temperature of the hot water was scarcely two thirds of that in the case of air; and it is as natural to think, that when filled with carbolic acid, it was the more sluggish motions of that gas which rendered the time one half longer than in the case of air; for the experiments of Dr Haycraft.

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1 Many eminent writers, without any evidence, take it for granted that the specific heat of a body depends on, or is in exact proportion to, its total or absolute heat; which is the more remarkable, considering that nothing is yet known, or likely ever to be, either of the real or relative values of the absolute heats of different bodies. But if we suppose, with far greater probability, that the specific heats of other bodies, as well as that of air, have no dependence on their volumes, this would enable us to account, in a more rational way than is usually done, for the heat accompanying friction, as, for instance, in Count Rumford's well-known experiments on the boring of cannon. Thus the grains of metal worn off by the intentionally blunt borer used on that occasion would be greatly compressed by the abrasion, and so might emit much heat without having their specific heats in the least impaired by the diminution of their volumes. In this way too the evolution of heat would continue as long as the wear and friction; which affords an explanation seemingly in accordance with the fact, without having recourse to the old notion that heat is a species of motion. The investigation in the text indeed implies that the absolute heat of air is indefinitely greater than its specific heat; and certainly many difficulties could be explained on the supposition that the same thing holds of bodies generally, or that all the heat we can impart to or abstract from bodies bears no proportion to their absolute heats. Hygrometry.

(Trans. Roy. Soc. Edin. vol. x. p. 195) are free from all such objections, and show that, under equal volumes and pressures, the specific heats of the different gases are equal, a result equally fatal to the conclusions which were deduced from the excessively complicated method of MM. Desormes and Clement. If, therefore, the experiments of Desormes and Clement are so very erroneous for comparing the specific heats of different gases, why should we put any confidence in them for that of the same gas under different pressures?

Experiments somewhat similar to those just noticed have been made by MM. de la Rive and Marcey, and described in the Annales de Chimie for May 1829; but in an article on the same subject in the next number of that journal, M. Dulong has shown, that in these experiments, from their being made on an exceedingly minute scale, the mass of air operated on was so very small, compared with that of the vessel, that they do not warrant any definite conclusion at all. We are scarcely better satisfied with the method which M. Dulong himself has there employed for estimating the specific heats of the gases from the frequency of their vibrations, as supposed to be registered by a kind of wind-instrument coupled with wheel-work, and called a sirene; because that method involves several questions not yet cleared up. But what we particularly object to is, that no allowance is made for the tendency which it is natural to think the vibrations of the materials of the wind-instrument itself must have to increase the frequency of the vibrations of the gas under examination; an oversight similar to what, as we shall by and by see, pervades the usually received theory of sound. Nor can there be a doubt that the vibrations of strings, wires, &c. in musical instruments are influenced by the vibrations of the materials by which they are stretched.

Having completed the intended investigations, it may now be useful to give some account of the experiments to which we have several times alluded; for ascertaining the value and constancy of the ratio of \( m \) to \( n \). We shall first give a familiar illustration of the principle, and then state more nearly the actual mode of experimenting. Suppose a vessel to be accurately closed, when occupied by air of the same temperature and pressure as that around it or in the apartment, and to be furnished with a gauge for showing any minute change of pressure. In this state let the apparatus be carried into another room of a little higher temperature, say \( m \) degrees warmer than the former; and then the gauge will soon indicate an increase of elasticity, which we may call \( m \) degrees. If the vessel admits of being now opened sufficiently, and shut again so promptly as just for the moment to allow the included air to regain the external or its original pressure, without affording time for its abstracting heat from the materials of the vessel, the gauge will in a little time indicate a second but much smaller increase of pressure, which we may call \( m - n \) degrees. The reason of this may be traced in a general way to the well-known fact, that air of whatever density is cooled by dilatation. The gauge, while indicating \( m \) degrees, shows the included air to be denser than that in the second apartment; and therefore, on opening the vessel, the superior elastic force within expels a portion of that air, leaving the remainder of course rarer than that of the first room, though still a little denser than that of the second; because it has been cooled, as the result shows, \( m - n \) degrees below the temperature of the second room. For at the instant of re-shutting the vessel, the elasticity of the included air is in equilibrium with the external pressure; but it must then be more dense than the air of the second apartment, otherwise, its temperature being lower, it could not balance the external pressure. On recovering therefore from the small and momentary depression of temperature, the excess of density shows itself by the gauge. The escape of a small portion of air while the vessel is open does not alter the result, because it only carries off its own heat. By this mode of operating, the ratio between the small quantities \( m \) and \( m - n \) can evidently be ascertained with incomparably greater exactness than by any thermometer whatever. The distinguished German philosopher Lambert had long ago contrived to operate on air in such a way that it showed the changes of its own temperature; and no doubt it has been the uncertainty attending the employment of thermometers in more recent researches on air, that has led to such strange and paradoxical results, and which has called in the aid of so many fanciful hypotheses regarding the nature of heat. Indeed there is no time for a thermometer of any sort acquiring the minute change of temperature denoted by \( m - n \).

Since we shall presently see that \( m \) is to \( n \) either exactly or very nearly as 4 to 3, it will conduce to greater simplicity if we now give this value to that ratio. But it is obvious, that during the small moment the vessel was open, the air which remained in it, having its temperature slightly depressed, could not lose heat, and had not time to gain any; so that the total heat in that remainder may be regarded as constant during the operation. Hence the same quantity of heat which had been sufficient to keep the air \( m \) degrees or \( 4^\circ \) above its original temperature while confined in the vessel, shows itself to be only able, while again put under the original pressure, to maintain an excess of \( n \) degrees or \( 3^\circ \) above that same temperature. The variation of heat, therefore, which would produce a given minute change, for instance, one degree in the temperature of air, and which variation is usually called its specific heat, must be one third greater when the air is free to change its volume under a constant pressure, than if confined in an inextensible vessel.

It is evident that the experiment would be essentially the same, if the vessel, in place of being brought from a colder apartment, were to have as much additional air injected into it as should make the gauge indicate \( 4^\circ \) above the external pressure, after the temperature of the included air has settled to that of the room; the rest of the process, as to opening and promptly shutting again the vessel, being as already described. Now, in either method it is obvious, that at the instant of suddenly re-shutting the vessel, the included air, being brought to an equilibrium with the atmosphere, had, with reference to pressure, lost all the additional \( 4^\circ \); while, as the second indication of the gauge, viz. \( 1^\circ \), shows it had only lost \( 3^\circ \) with regard to density, one of the lost degrees of pressure being therefore due to momentary depression of temperature. Hence, the height of the barometer, or whole pressure, is to the variation of pressure denoted by \( 4^\circ \), as \( p \) to \( dp \). Also the height of the barometer, or whole density, is to the variation of density denoted by \( 3^\circ \), as \( \rho \) to \( d\rho \). Consequently, \( p : 3dp :: \rho : 4d\rho \).

Such is nearly the mode of experimenting followed by Mr Meikle, as detailed at length in the Edinburgh Phil. Journ. for April 1827, and more recently repeated with an improved apparatus, fully as large as the former one, which contained 2810 cubic inches, but with the advantage of having four apertures, amounting together to twenty-five square inches, which can be both opened and shut again so promptly, that the time of their being open is only a small fraction of a second. Something similar had been previously practiced, though with a less perfect apparatus (Journal de Physique for Nov. 1819, p. 331), by MM. Desormes and Clement, and had likewise, at the desire of Marquis de Laplace (Mécanique Céleste, livre xii. chap. 3, and Comm. des Temps for 1825, p. 372), been adopted by MM. Gay-Lussac and Welter, who continued it through a great range both of temperature and pressure; but they do not make the simultaneous variations of density and pressure Hygrometry.

Exactly such, that \( p : 3dp :: \varepsilon : 4d\varepsilon \), which is very nearly the relation obtained by Mr Meikle from a mean of many experiments, and with either apparatus; but they make \( p : 3dp :: \varepsilon : 4\cdot1244d\varepsilon \). The difference is not very considerable; and the following consideration, we think, renders it extremely probable that the former is the true relation. Sir Isaac Newton has shown (Principia, lib. ii. prop. 23), that if in an elastic fluid the cube of the pressure vary as the \( r + 2 \) power of the density, the particles should repel each other with forces inversely as the \( r \)th powers of their distances; and similar investigations and results may be seen in other elementary works. Now, these experiments of the French philosophers just named make the cube of the pressure proportional to the \( 4\cdot1244 \) power of the density, as is evident if we put \( 3 \) and \( 4\cdot1244 \) in place of \( n \) and \( m \) in art. 3. Hence \( r = 2\cdot1244 \), and therefore the particles would repel each other with forces inversely as the \( 2\cdot1244 \) powers of their distances; a law of which there is no known parallel in nature. But if the ratio of \( n \) to \( m \) were that of \( 3 \) to \( 4 \), and these numbers were substituted as indices in art. 3, we should have \( \left( \frac{p}{p'} \right)^3 = \left( \frac{\varepsilon}{\varepsilon'} \right)^4 \), or the cube of the pressure varying as the fourth power of the density; and consequently, the repulsion between the particles of the air would vary inversely as the squares of their distances, which is the only known law of repulsion, and most likely the only one which exists.

It had long been well known in a general way, that when air has its volume or bulk changed so suddenly as to afford little or no time during the process for its either imparting heat to or receiving it from surrounding bodies, the pressure is at that instant changed in a much higher ratio than the density is. This was quite sufficient to render it certain, that whatever might be precisely the true law of repulsion, it must follow something very different from the reciprocal of the simple distance, which supposes the pressure and density to vary in the same ratio. For it was as well known, that during cases where the pressure has varied in the same ratio as the density, time enough has always elapsed for the air either imparting to or receiving from surrounding bodies as much heat as it may either have evolved by compression or absorbed by dilatation; because compression, by tending to warm the air, induces it to give out heat, and dilatation, by tending to cool the air, induces it to receive heat. But when, from cases in which the pressure had varied in the same ratio as the density, Newton inferred that the particles of air repelled each other with forces inversely as their simple distances, he was quite excusable; because the facts just noticed were not known in his time, nor were they indeed attended to till towards the end of last century. The like excuse, however, cannot so well be pleaded for Dr Dalton, who, in speculating on the constitution of the atmosphere so lately as in the Phil. Trans. for 1826, just adopts the law of repulsion deduced by Newton, and without making the slightest objection to it on the score now stated. The French savans, again, in having virtually made the repulsion vary inversely as the \( 2\cdot1244 \) power of the distance, seem to have run a little into the opposite extreme. But when they adopted that conclusion, they were perhaps influenced a little by Laplace's theory of sound, which required something of the sort to help it out, and for which indeed the experiments of Gay-Lussac and Welter were purposely undertaken. The defect of the theory, we presume, lies rather in its not including the share which it is likely the re-action of the earth's surface has in accelerating the transmission of sound. For it seems reasonable to think, that since the air presses strongly on the earth's surface, it must, while propagating sound, both set that surface a vibrating, and, in return, have its own vibrations accelerated thereby; because the vibrations of the earth's surface should incline to be more frequent than those of air. Such at least seems to be the case with the vibrations of solids and liquids generally; though these again differ widely among themselves, and should of course affect the velocity of sound differently. According to this suggestion, the louder or the more intense the sound, the more fully will the earth's surface be brought into action, and consequently the greater, ceteris paribus, should be its accelerating influence. A similar defect, as we hinted above, seems to attach to the many attempts which have been made to determine the frequency of the vibrations of elastic fluids by means of wind-instruments; no allowance being made for the influence which it is likely the vibrations of the materials composing the wind-instruments have on the frequency of the vibrations of the gas under examination.

We shall now enter on the consideration of hygrometers which are formed of materials comparatively free from decay, which are constant or consistent in their indications, and which, in short, seem in a great measure to possess the first five of the properties already specified, which Saussure considered necessary to a perfect hygrometer: as for his sixth, we regard it as supererogatory. The fact that humid air readily wets bodies which are colder than itself, such as stones and walls at the commencement of a thaw, must have been familiar to mankind from the remotest antiquity; though it has not been long known that dew or hoar-frost affords the most universal example of this all the world over; being moisture deposited on bodies which have been sufficiently cooled by radiation below the temperature of the incumbent air. The ancients appear to have conjectured that a copious deposition of moisture on cold bodies prognosticated bad weather; but the first step perhaps towards applying this principle to the construction of a hygrometer was made by the Florentine academicians, who having suspended in the open air a conical vessel filled with snow or powdered ice, supposed the humidity of the air to be proportional to the quantity of moisture which, being condensed on the exterior surface of this vessel, trickled down its sides, and dropt from the apex of the cone. This, however, could afford but a very vague estimate of the humidity of the air; because the quantity of moisture thus collected must obviously have depended in a great measure on the velocity of the wind; and such an estimate would be still more erroneous, or rather useless altogether, in the time of frost. The same idea was farther improved upon by M. Leroy of Montpellier, who, by dropping ice into water contained in a vessel with a bright exterior surface, gradually lowered its temperature, till dew began to be deposited from the contiguous air on that surface. Saussure substituted sal ammoniac for ice, and different salts have been employed by others for the same purpose. The temperature to which the vessel is thus brought at the moment of incipient deposition, is obviously the temperature to which, if the air were cooled under the same pressure, the vapour in it would be in a state of saturation, or ready to deposit dew upon any thing in the least degree colder than itself. Such temperature is therefore denominated the dew-point. Did the air, in cooling, undergo no diminution of volume, it would not be brought to a state of saturation with moisture, till it were cooled below \( t + 448 \) nearly in the ratio of \( 1 + \frac{t + 448}{8600} \) to \( 1 \) than that which brings it to the dew-point. Some writers do not seem aware of there being any difference between these points of saturation; and others have such confused notions of it, that not unfrequently they transpose them; though no- thing is more certain than that these temperatures cannot be the same, and that the dew-point is the higher of the two. For if \( t \) be the actual temperature of the air, and \( t' \) the dew-point, since the pressure is the same in both cases, the actual density of the air is to its density when cooled to the dew-point, in the inverse ratio of \( t + 448^\circ \) to \( t' + 448^\circ \), as was shown above regarding the expansion of air; but since all elastic fluids yet tried expand or contract at the same rate by the same change of temperature, the density of the vapour at the dew-point must therefore be greater in the above ratio than its density at the actual temperature, which is the same as its density would be were the air cooled without shrinkage. This, however, is not meant to prove the above ratio to be the very law of nature.

The following table is for facilitating computations of this kind. The first column is the Fahrenheit temperature \( t \); the second the maximum force \( f \) of aqueous vapour for that temperature; the third the corresponding weight of moisture in a cubic foot expressed in grains.

The fourth column, computed from the formula

\[ \frac{t + 448}{480} \]

shows the ratio in which an elastic fluid is expanded or contracted by having its temperature changed from \( 32^\circ \) to \( t \); and this column, being everywhere in the ratio of the temperature reckoned from \( -448^\circ \), may therefore denote either the volume of a given mass of elastic fluid under a constant pressure, or the pressure under a constant volume, the unit of each being at \( 32^\circ \). The second column is computed from the formula which M. Biot has deduced from Dr. Dalton's experiments; viz.

\[ \log_e = 1.4771213 - 0.0085412197 (212 - t) - 0.0000208109 (212 - t)^2 + 0.0000000058 (212 - t)^3; \]

but we have slightly increased a few of the numbers next zero, to correspond with the experiments of Gay-Lussac, because those of Dr. Dalton did not go lower than \( 32^\circ \).

Vapours of all sorts, so far as yet tried, are found to observe the general laws of elastic fluids, in having the density directly as the pressure, and inversely as \( t + 448 \); and from the experiments of Dr. Rice it appears that a cubic foot of water at \( 40^\circ \) weighs 437,272 grains; and this again M. Gay-Lussac found to be 1700 times heavier than a cubic foot of aqueous vapour at \( 21^\circ \), which therefore weighs 257,2188 grains. Hence, to obtain the Hygrometry numbers for the third column, we have

\[ \frac{30}{212 + 448} : \frac{f}{t + 448} :: 257,2188 : \frac{5658,61f}{t + 448}, \]

the number of grains in a cubic foot of aqueous vapour in a state of saturation, at the temperature \( t \).

But when the vapour is not in a state of saturation, as, for instance, when the actual temperature of the air is \( 60^\circ \), and the dew-point only \( 40^\circ \), we proceed thus:—Opposite \( 40^\circ \) in the first column of the table we find \( 2644 \) inch in the second for the actual force of vapour in the air; but from what has been shown above regarding the expansion of elastic fluids, the density at \( 60^\circ \), corresponding to a force of \( 2644 \), must be less than if the temperature were \( 40^\circ \), in the ratio of \( 40 + 448 \) to \( 60 + 448 \), or of \( 1:0167 \) to \( 1:0583 \) (viz. using the numbers in the fourth column opposite \( 40^\circ \) and \( 60^\circ \)). We must therefore reduce in that ratio the maximum weight in a cubic foot at \( 40^\circ \), namely, \( 3:066 \) grains, which will make it \( \frac{1:0167}{1:0583} \times 3:066 = 2:945 \) grains for the actual weight of moisture in the air, corresponding to a temperature of \( 38^\circ 8 \); so that, had the air been cooled down to \( 38^\circ 8 \), without shrinkage, or under the original volume, the vapour would have been brought to a state of saturation. The temperature \( 38^\circ 8 \), as already observed, is lower than the dew-point by very nearly \( \frac{t + 448}{8600} \) times the difference between the dew-point and the temperature of the air. Thus \( 38^\circ 8 = 40^\circ - (60 - 40) \times \frac{508}{8600} \); which affords a ready mode of computing this lower point of saturation without the aid of any table.

It is much more convenient to use the grains in a cubic foot than the small fraction of a grain in a cubic inch; because the latter requires more figures to express it with the same accuracy. But it is not so much from pretensions to superior exactness that we use so many decimal places in these columns, as to render the differences of the numbers more uniform, which is of consequence when there is any occasion for taking proportional parts, or interpolating between them.

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1 The committee of the Royal Academy of Sciences at Paris, who made a very elaborate and extensive series of experiments on the force of steam in 1829, as described at length in the Ann. de Chim. for January 1830, give the following formula:

\[ \epsilon = \left(1 + 0.007153(T - 100)\right)^4, \]

where \( \epsilon \) is the elasticity in atmospheres, and \( T \) the temperature centigrade. This expression, however, becomes far too small at low temperatures, and vanishes altogether at the freezing point of mercury. M. Roche, again, makes

\[ \log_e = \frac{T - 100}{T + 266.67} \times 5.48. \]

But neither can any expression of this form be the law of nature; because, besides erring considerably at temperatures within the range of observation, it would require the density of saturated steam to reach a maximum, and then decrease; so that some of it would become liquid by the addition of more heat, which is quite incredible. Indeed every formula which, so far as we know, has yet been published, for expressing the force of steam, is liable to some such objections. | Temperature | Force in Inches | Grains in a Foot | Ratio of Expansion | Temperature | Force in Inches | Grains in a Foot | Ratio of Expansion | |-------------|-----------------|------------------|-------------------|-------------|-----------------|------------------|-------------------| | 0° | 0.0622 | 786 | 0.9333 | 50° | 0.3735 | 4.244 | 1.0375 | | 1 | 0.0443 | 810 | 0.9354 | 51 | 0.3864 | 4.382 | 1.0396 | | 2 | 0.0665 | 836 | 0.9375 | 52 | 0.3998 | 4.524 | 1.0417 | | 3 | 0.0888 | 864 | 0.9396 | 53 | 0.4136 | 4.671 | 1.0438 | | 4 | 0.0713 | 893 | 0.9417 | 54 | 0.4278 | 4.822 | 1.0458 | | 5 | 0.0740 | 925 | 0.9438 | 55 | 0.4425 | 4.978 | 1.0479 | | 6 | 0.0769 | 957 | 0.9458 | 56 | 0.4576 | 5.138 | 1.0500 | | 7 | 0.0798 | 992 | 0.9479 | 57 | 0.4733 | 5.303 | 1.0521 | | 8 | 0.0829 | 1.028 | 0.9500 | 58 | 0.4894 | 5.473 | 1.0542 | | 9 | 0.0860 | 1.065 | 0.9521 | 59 | 0.5060 | 5.648 | 1.0562 | | 10 | 0.0893 | 1.103 | 0.9542 | 60 | 0.5232 | 5.828 | 1.0583 | | 11 | 0.0927 | 1.143 | 0.9563 | 61 | 0.5409 | 6.013 | 1.0604 | | 12 | 0.0962 | 1.184 | 0.9583 | 62 | 0.5591 | 6.204 | 1.0625 | | 13 | 0.0999 | 1.226 | 0.9604 | 63 | 0.5780 | 6.400 | 1.0646 | | 14 | 1.036 | 1.270 | 0.9625 | 64 | 0.5974 | 6.602 | 1.0667 | | 15 | 1.076 | 1.315 | 0.9646 | 65 | 0.6173 | 6.810 | 1.0688 | | 16 | 1.116 | 1.361 | 0.9667 | 66 | 0.6380 | 7.024 | 1.0708 | | 17 | 1.158 | 1.409 | 0.9688 | 67 | 0.6592 | 7.243 | 1.0729 | | 18 | 1.201 | 1.459 | 0.9708 | 68 | 0.6811 | 7.469 | 1.0750 | | 19 | 1.246 | 1.510 | 0.9729 | 69 | 0.7036 | 7.702 | 1.0771 | | 20 | 1.293 | 1.563 | 0.9750 | 70 | 0.7269 | 7.941 | 1.0792 | | 21 | 1.341 | 1.618 | 0.9771 | 71 | 0.7508 | 8.186 | 1.0813 | | 22 | 1.391 | 1.674 | 0.9792 | 72 | 0.7755 | 8.439 | 1.0833 | | 23 | 1.442 | 1.733 | 0.9813 | 73 | 0.8009 | 8.699 | 1.0854 | | 24 | 1.495 | 1.793 | 0.9833 | 74 | 0.8271 | 8.966 | 1.0875 | | 25 | 1.551 | 1.855 | 0.9854 | 75 | 0.8541 | 9.241 | 1.0896 | | 26 | 1.608 | 1.919 | 0.9875 | 76 | 0.8818 | 9.523 | 1.0917 | | 27 | 1.667 | 1.986 | 0.9896 | 77 | 0.9104 | 9.813 | 1.0938 | | 28 | 1.728 | 2.054 | 0.9917 | 78 | 0.9399 | 10.111 | 1.0958 | | 29 | 1.791 | 2.125 | 0.9938 | 79 | 0.9702 | 10.417 | 1.0979 | | 30 | 1.856 | 2.197 | 0.9958 | 80 | 1.0014 | 10.732 | 1.1000 | | 31 | 1.924 | 2.273 | 0.9979 | 81 | 1.0335 | 11.055 | 1.1021 | | 32 | 1.993 | 2.350 | 1.0000 | 82 | 1.0666 | 11.388 | 1.1042 | | 33 | 2.066 | 2.430 | 1.0021 | 83 | 1.1006 | 11.729 | 1.1063 | | 34 | 2.140 | 2.513 | 1.0042 | 84 | 1.1356 | 12.079 | 1.1083 | | 35 | 2.218 | 2.598 | 1.0062 | 85 | 1.1716 | 12.439 | 1.1104 | | 36 | 2.297 | 2.686 | 1.0083 | 86 | 1.2097 | 12.808 | 1.1125 | | 37 | 2.380 | 2.776 | 1.0104 | 87 | 1.2468 | 13.185 | 1.1146 | | 38 | 2.465 | 2.870 | 1.0125 | 88 | 1.2850 | 13.577 | 1.1167 | | 39 | 2.553 | 2.966 | 1.0146 | 89 | 1.3264 | 13.977 | 1.1187 | | 40 | 2.644 | 3.066 | 1.0167 | 90 | 1.3679 | 14.387 | 1.1208 | | 41 | 2.738 | 3.168 | 1.0187 | 91 | 1.4106 | 14.809 | 1.1229 | | 42 | 2.835 | 3.274 | 1.0208 | 92 | 1.4544 | 15.241 | 1.1250 | | 43 | 2.935 | 3.382 | 1.0229 | 93 | 1.4995 | 15.684 | 1.1271 | | 44 | 3.038 | 3.495 | 1.0250 | 94 | 1.5459 | 16.140 | 1.1292 | | 45 | 3.145 | 3.610 | 1.0271 | 95 | 1.5935 | 16.607 | 1.1313 | | 46 | 3.256 | 3.729 | 1.0292 | 96 | 1.6425 | 17.086 | 1.1333 | | 47 | 3.368 | 3.851 | 1.0313 | 97 | 1.6929 | 17.577 | 1.1354 | | 48 | 3.488 | 3.979 | 1.0333 | 98 | 1.7446 | 18.081 | 1.1375 | | 49 | 3.609 | 4.109 | 1.0354 | 99 | 1.7978 | 18.598 | 1.1396 | | 50 | 3.735 | 4.244 | 1.0375 | 100 | 1.8524 | 19.129 | 1.1417 |

The principles already explained will make the construction and use of Professor Daniell's elegant instrument easily understood. It is represented in its full dimensions in fig. 8, Plate CCXCV, where \(a\) and \(b\) are two thin glass balls of 1.25 inch in diameter, connected by a tube having a bore of about 1.25 inch. The tube is bent at right angles over the two balls; and the arm \(be\) contains a small thermometer whose bulb, which is of an oval form, descends into the ball \(b\). This ball having been about two thirds filled with ether, is heated over a lamp till the liquid boils, and the vapour issues from the capillary tube \(f\) on the under side of the ball \(a\). The vapour having expelled the air from both balls, the capillary tube \(f\) is hermetically closed by the flame of a lamp. This process is familiar to those who are accustomed to blow glass, and may be known to have succeeded after the tube has become cool, by reversing the instrument, and taking one of the balls in the hand, the heat of which will cause the ether to boil rapidly, and pass wholly over by distillation into the other ball. The ball \(a\) is now to be covered with a piece of muslin. The stand \(gl\) is of brass, and the transverse socket \(i\) is made to hold the glass tube in the manner of a spring, allowing it to turn and be taken out with little difficulty. Another small thermometer \(k\) is inserted into the pillar of the stand. The manner of using the instrument is this:—After having driven all the ether... Hygrometry.

Into the ball b by the heat of the hand applied to the ball a, the instrument is to be placed at an open window, or out of doors, with the ball b so situated, as that the surface of the liquid may be upon a level with the eye of the observer. A little ether is then to be dropped upon the covered ball. Evaporation immediately takes place, which, by abstracting heat, cools the ball a, and causes a rapid and continuous condensation of the ethereal vapour within it, together with a diminution of pressure. The consequent evaporation from the included ether produces a depression of temperature in the ball b, the degree of which is measured by the thermometer d. This action is almost instantaneous, and the thermometer begins to fall in two seconds after the ether has been dropped. A depression of thirty or forty degrees is easily produced, and the ether may be sometimes seen to boil when the thermometer is below the zero of Fahrenheit. So soon as the ball b is cooled by this artificial process down to the dew-point of the surrounding air, a condensation of the atmospheric moisture takes place upon its surface, and this first makes its appearance in a narrow ring of dew on a level with the surface of the ether. The temperature at which this occurs, viz. the dew-point, is to be carefully noted. A little practice may be necessary to seize the exact moment of first deposition, but certainty is very soon acquired. It is advisable, when the ball b of the instrument has been made of transparent glass, to have some dark object behind it, such as a house or a tree, because the cloud is not so readily perceived against the sky or open horizon. The depression of temperature is first produced at the surface of the liquid, where evaporation takes place, and the currents which immediately ensue to effect an equilibrium are very perceptible. We may here remark by the by, that since the covered ball a must be fully the colder of the two, there is reason to think, that while it is throwing off and furnishing latent heat for ethereal vapour, it is very likely condensing aqueous vapour and absorbing its latent heat. The bulb of the enclosed thermometer d is but partially immersed in the ether, with the view of making the line of greatest cold pass through it; but this we shall find to be a faulty arrangement. In very damp or windy weather, the ether should be very slowly dropped upon the ball, otherwise the descent of the thermometer will be so rapid as to render it extremely difficult to be certain of the degree at which deposition commences. In dry weather, on the contrary, the ball requires to be well wetted more than once, to produce a sufficient cold. If at any time there should be reason to suspect the accuracy of an observation, it may, according to Mr Daniell, be corrected by observing the temperature at which the dew upon the glass again disappears: the mean of the two observations should give the true result; because their errors, he thinks, if any, should lie in contrary directions. This, however, is on the supposition that the error lies all with the observer, and that the instrument itself is faultless; whereas we shall shortly see reason to conclude that, unless it be agitated during an observation, it has a tendency to give the dew-point too high, owing to every part of the bulb of the included thermometer not being alike exposed to the cooling effects of the ether. It is obvious that care should be taken not to permit the breath to come into contact with the glass.

Mr Daniell's hygrometer may also be applied to artificial atmospheres, and experiments on air or other gas confined in a vessel. Fig. 9 represents a receiver and hygrometer prepared for this purpose; and the following is the manner in which they were fitted up. A hole is perforated in the side of the receiver, through which the tube proceeding from the ball within it containing the thermometer is first passed, and then welded by means of a lamp to the tube attached to the other ball outside the receiver. The stem is secured in the hole of the receiver with cement, the ether is boiled, and the capillary tube closed, as before described. The external ball is then to be covered with muslin, and ether being dropped upon it, the consequent evaporation produces, in the manner already explained, a corresponding degree of coldness in the internal ball. The state of humidity within may be ascertained by noting the temperature at which dew begins to appear on that ball. In delicate experiments, a lighted taper in a glass lantern, placed behind the instrument, renders the deposition more easily visible, and ensures accuracy. The hygrometric properties of any substance, or its power of absorbing moisture, may thus be readily estimated, by placing it under the receiver, and marking the fall which it occasions in the dew-point. By means of this apparatus Mr Daniell made a variety of experiments, from which it appeared, as Deluc, Dalton, and others had asserted, that the quantity of moisture which can exist in a given volume depends solely on the temperature, and is not influenced by the presence or density of air or other elastic fluids, provided no chemical action occur.

There have been various attempts to improve upon Mr Daniell's hygrometer, or to contrive a more simple one, improving which should serve the same purpose. About ten years ago, several instruments, essentially the same in principle, though differing widely in contrivance from Mr Daniell's, were proposed in different quarters with this view. The leading features in their construction are, to cover partially the bulb of a large thermometer with muslin, silk, cambric, or the like; to wet this with ether; and to observe at what degree of that thermometer moisture is deposited on the uncovered part of its bulb. A more simple construction for directly observing the dew-point was scarcely to be expected, but unfortunately it was soon found to be very fallacious. For, owing to the uncovered part of the bulb not being directly exposed to the cooling effects of the evaporation, its temperature, viz. the dew-point, is generally several degrees higher than the mean temperature of the bulb, or that indicated on the scale of the thermometer; so that such instruments generally give a dew-point considerably below the truth, and the error is found to be greater when the bulb is of an elongated or cylindrical form than when spherical. This error may be made manifest in several ways, but the preferable one seems to be to observe the dew-point at the same time by the method of Leroy, as improved by Saussure and Dalton, namely, to cool down water in a bright vessel by dropping in colder water, ice, or salts, and to stir it with a thermometer till dew just begin to appear on the exterior surface of the vessel. The thermometer will at that instant indicate the dew-point with great accuracy if the vessel is thin, and especially if of metal.

The discovery of such a defect in these instruments led to a careful examination of Mr Daniell's hygrometer by the same test; and the result was, that it is liable to the contrary error of giving the dew-point above the truth. For since in that instrument the deposition occurs in a narrow ring or zone on a level with the surface of the enclosed ether, which, during the cooling, is considerably colder at the surface than beneath; and since the elongated bulb of the enclosed thermometer is only half immersed in this ether, it is evident that scarcely half of this bulb is subjected to so great a cold as that which produces the deposition of moisture. As to any cooling effect of the ethereal vapour on the upper half of the ball, it must be extremely feeble compared with the cooling influence of that liquid itself, as is evident from the effect which agitating the ether round the whole bulb of the thermometer has in lowering its indication. In place therefore of an observation with this hygrometer being Hygrometry—“simple, expeditious, easy, and certain,” it is evident, that unless the instrument is shaken, or the observation made so slowly and cautiously as to allow the bulb of the included thermometer time to become all of one temperature, it cannot fail to give the dew-point too high; so that the more clever or expeditious any one fancies himself to be in using this instrument, so much the farther his observation likely to be from the truth.

A substitute for this instrument, preferable to any of the foregoing, has been contrived by Mr John Adie, and is described in the *Edinburgh Journal of Science* (new series, vol. i. page 60). A thermometer having a small bulb enclosed in an exterior bulb or case of black glass, which is covered with silk, excepting a small space about a quarter of an inch in diameter, where the deposition is to be observed. The space between the outer and inner bulbs is nearly filled with any liquid not liable to freeze by the depression of temperature required for finding a dew-point, as alcohol, mercury, linseed oil, &c. When an observation is to be made, ether is applied to the silk, and the instrument is kept in a state of gentle agitation, to render the inner and outer bulbs all of one temperature. With this instrument Mr Adie obtained constant results, not differing more than half a degree from Leroy’s method, already described. The following table exhibits the results in twenty-eight cases, as observed with five different dew-point instruments. The first column is the temperature of the air; the second the dew-point, as observed by Leroy’s method; the third, by Mr Adie’s instrument; the fourth, by Mr Daniell’s; the fifth, by the large thermometer, having a round bulb partially covered with muslin; the sixth, by the same kind of thermometer with an elongated or cylindrical bulb.

| Temperature of the Air | Leroy's Method | Adie's | Daniell's | Spherical Bulb | Long Bulb | |------------------------|---------------|--------|-----------|----------------|----------| | 53° | 45° | 45° | 46° | 45° | 41° | | 55 | 44 | 43-5 | 45 | 41 | 39 | | 52 | 44 | 44 | 47 | 42 | 39 | | 54 | 41 | 41 | 42 | 37 | 33-5 | | 63 | 54 | 53-5 | 55 | 50 | 47 | | 50 | 43 | 43 | 44 | 41 | 40 | | 54 | 44 | 43-5 | 45 | 40 | 40 | | 51 | 45 | 45 | 47 | 42 | 41 | | 42 | 32 | 32 | 32 | 30 | 29 | | 55 | 46 | 46 | 47 | 44 | 40 | | 47 | 39-5 | 39 | 41 | 38 | 34 | | 51 | 43 | 43 | 46 | 41 | 35 | | 50 | 38 | 38 | 41 | 35 | 32 | | 42 | 28 | 28 | 31 | 23 | 20 | | 34 | 27 | 27 | 32 | 24 | 18 | | 48 | 39 | 39 | 46 | 37 | 32 | | 47 | 38-5 | 38-5 | 42 | 32 | 30 | | 42 | 30 | 30 | 34 | 23 | 20 | | 45 | 35 | 35 | 39 | 32 | 25 | | 42 | 33 | 33 | 38 | 29 | 26 | | 47 | 42 | 42 | 43 | 37 | 35 | | 43 | 30 | 30 | 35 | 27 | 25 | | 41 | 32 | 32 | 35 | 29 | 25 | | 39 | 26 | 26 | 29 | 23 | 20 | | 39 | 26 | 26 | 29 | 22 | 22 | | 38 | 26 | 26 | 31 | 22 | 22 | | 28 | 21 | 20-5 | 24 | 17 | 16 | | 32 | 17-5 | 17 | 24 | 14 | 13 |

Sum 1286 1009-5 1006-5 1090 915 824-5

Mean 45-9 36-03 35-93 38-93 31-25 29-43

Mean errors —0-1 +2-9 -4-78 -6-6 brings the bulbs as near each other as if the covered one were only a little above the stem of the enclosed thermometer. Whether any chemical action may take place between the aqueous and ethereal vapours, which could sensibly affect the deposition of dew, we could not pretend to say; but it is natural to think that the expansive force of the ethereal vapour should distend or dilate the air and moisture, which would tend to lower the dew-point. Mr Adie's experiments, it is true, seem to give the dew-point the same as by Leroy's method; but in his cases given above, the dew-point is generally so little below the temperature of the air as to have required very little ether to produce the requisite cooling; so that it may have been owing to the comparatively feeble state of the ethereal vapour that the dew-point was not sensibly affected; or possibly the chemical and mechanical effects of the ether on the dew-point might be opposed to each other. But it is surely more safe to avoid any risk of this sort altogether. With any sort of dew-point instrument, it must be difficult to observe at low temperatures the precise degree at which the vapour is cooled to saturation, owing to its extreme tenacity. For unless the bright surface be sensibly colder than the air to which it is presented, the commencement of deposition is not likely to be readily noticed in very attenuated vapour.

Dr James Hutton seems to have been the first who thought of applying the comparison of the different indications which a thermometer exhibits in a dry and in a moistened state to the purposes of hygrometry. With this view he had a thermometer enclosed in a glass tube hermetically sealed, which he first held in a proper situation till it acquired and showed the temperature of the air. Then having dipped it in water, he held the end of the tube which contained the bulb towards the current of air, and observing how much the thermometer had been lowered by evaporation, he regarded the depression as a measure of the dryness of the air. This view of the matter, though not quite correct, was a wonderful step, considering how little was then known regarding the laws which regulate the diffusion of aqueous vapour in air or other elastic fluids. But instead of employing only one thermometer, and enclosing it, as Dr Hutton did, in a glass tube, it is found not only more convenient, but conducing to greater accuracy, to use two thermometers; one of which notes the actual temperature of the air, while the other, having its bulb covered with muslin, silk, cambric, or the like, and moistened with pure water, shows the temperature as depressed by evaporation. We have found it to be still more convenient to have both thermometers mounted on one broad and doubly graduated scale, and both might be of the self-registering sort. Soft paper has sometimes been used to cover the thermometer; but if it contain any soluble matter, it is apt to render the water impure, and vitiate the results. In short, whatever sort of covering is used, care should be taken to have it both clean and free from every thing which may affect the purity of the water. Thus the thermometer is found to be much less cooled by evaporation when moistened with brackish water than with fresh. Some cover the bulbs of both thermometers, with the view of having the surfaces as nearly alike as possible, and of one colour, to obviate any unequal effects of light or radiation; the nearer to white of course the better.

This sort of hygrometer, after having been sadly neglected for thirty years, at least in any thing near its original form,1 has at length become an object of interest both here and on the Continent, particularly in Germany, where it has been dignified with the name of the Psychrometer. The British Association too has repeatedly expressed a desire to receive a satisfactory exposition of the theory of this instrument, and has requested observers to institute comparative experiments between its indications and the corresponding dew-points, as obtained by the methods already described. So that, when once comparisons of this sort have been made in circumstances sufficiently varied for the different states of the air, this hygrometer, from the durability and simplicity of its construction, the extreme facility with which it can be used, and the consistency of its indications in like states of the air, bids fair to come into more general use than any other; and this, we should think, is likely to be the case in a very few years. One of its most remarkable features, and which adds greatly to its value, is, that its indications are scarcely affected by any ordinary wind. They are, however, as will be noticed after, somewhat under the influence of the atmospheric pressure, but so slightly, that at the same place variations of pressure may in ordinary cases be neglected. When the moist thermometer is below 32°, about an eighth part of its depression below the temperature of the air is owing to the expense of heat for liquefying the ice previously to evaporation; the heat of liquidity being about a seventh part of the latent heat of the vapour; but this is a point which, so far as we know, has not yet been examined by any direct experiments.

When this instrument is first exposed to the drying influence of air, in which the aqueous vapour is not already in a state of saturation, evaporation takes place, and lowers the temperature of the moist bulb, by abstracting heat from it for the formation of additional vapour; but a limit is soon set to the fall of temperature by the surrounding air, which, in successively touching the wet and colder surface, imparts heat to it; and also no doubt by the warmer surrounding bodies throwing in a little heat upon the colder bulb by radiation. The heat thus imparted and thrown in is next to all we can think of as being continually supplied to the moist surface, and spent in the formation of new vapour, the supply being of course exactly equal to the expenditure, which depends on the drying influence of the air; and so does the difference of temperature, though the precise relations between them have not yet been determined. It might indeed be supposed that the stem of the thermometer should convey a little heat to the moist bulb; but the stem being of glass, is a bad conductor, and any heat which it supplies must be very inconsiderable, since it makes no sensible difference whether we apply a wet covering to the bulb alone, or continue it along a part of the stem. However, in the Edinburgh Encyclopaedia, art. Hygrometry, Dr Anderson advances the doctrine, that the moist bulb itself furnishes all the heat spent in the formation of new vapour; whereas we cannot conceive how it can continue to furnish the smallest portion of heat after the process has fairly commenced, any more than a hot iron could continue to furnish heat to the air after it has been cooled down to the temperature of the air. Dr Anderson has, in the same article, and afterwards in different volumes of the Edinburgh Phil. Jour. (first series), given a variety of investigations connected with the use of the moist-bulb hygrometer; but as they involve the idea that the capacity of air for moisture is, ceteris paribus, proportional to the barometric pressure, his results necessarily diverge widely from the truth, when applied to cases materially different from those on which they are founded.

As already mentioned, the extent of the depression of temperature is scarcely affected by any ordinary wind; but unless the heat which surrounding bodies throw in

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1 A description of the late Sir John Leslie's hygrometer will be found under the article Meteorology. Hygrometry.

By radiation on the colder bulb be quite inappreciable, this constancy of depression, so far from proving that the cooling influence of evaporation is independent of the wind, would rather argue that it is less as the velocity of the wind is greater. For since evaporation increases with the wind, while radiation is believed to be independent of it, it follows that the heat supplied by radiation not increasing in the same ratio as the expenditure or new vapour does, the depression, in place of being constant, as it is found to be, ought to increase with the velocity of the wind. Hence either the heat supplied by radiation is inconsiderable, or, which is more probable, the cooling influence of evaporation is less as the velocity of the wind is greater. From experiments described by Mr Meikle in the Edinburgh Phil. Jour. for January 1827, it appears that giving a pretty rapid motion to a moist thermometer in air confined over sulphuric acid, tended considerably to increase the depression of temperature; but it may be questioned whether this was not owing to the agitation of the apparatus enabling the acid to render the air drier.

Philosophers are by no means agreed regarding the theory of this instrument, which, as we shall afterwards see, is involved in great difficulty and obscurity; but this is of less consequence, since a complete theory does not seem necessary to enable us to apply it to hygrometric purposes. For when once the dew-points corresponding to a sufficient variety of indications of the wet and dry thermometers and of the barometer have been well ascertained, a table of dew-points may be constructed from them, having for its entries or arguments the indications of the wet and dry thermometers, corrected, if necessary, for the particular pressure; so that, when aided by such a table, the indications of the wet and dry thermometers, and of the barometer, may obviously give us the dew-point, whether we know anything of the theory or not.

The results of experiments determining the dew-point for a considerable number of indications of the wet and dry thermometers, and under various pressures, though principally at pretty high temperatures, are given in a Calcutta journal, Gleanings in Science, Nos. II. and III. 1829, and in the Edinburgh Phil. Jour. for October 1833, from which we have obtained the following table. The sixth column is derived from the formula

\[ f_t' = \frac{(f_t + 65372)(t - e)}{175438} = f_t' \]

where \( t \) is the Fahrenheit temperature of the air, \( e \) that of the moist bulb, and \( f_t' \) the dew-point; and \( f_t, f_t', f_t'' \) are the forces of aqueous vapour in a state of saturation at these temperatures respectively.

| Barometer | Temperature of the Air | Temperature of Moist Bulb | Difference or Depression | Observed Dew-point | Computed Dew-point | Difference | Remarks | |-----------|------------------------|---------------------------|--------------------------|--------------------|--------------------|------------|---------| | 29-75 | 67°-2 | 52°-0 | 15°-2 | 35°-7 | 35°-7 | 0 | Dr Anderson's experiments. | | 30-025 | 56°-4 | 49-5 | 6°-9 | 39-5 | 40-7 | +1-2 | Observations made in India at the level of the sea by means of Leslie's and Daniell's hygrometers. | | 29-85 | 65°-0 | 51-5 | 13°-5 | 35-45 | 36-6 | +1-1 | Do. on hills in the south of India. |

The dew-points in the sixth column do not differ very materially from observation; but the temperatures from which they were computed had first to be corrected for the barometric pressure, being different from thirty inches. The precise rule for estimating such a correction is as yet unknown; but it appears that, for the same temperature of the moist bulb, the difference between it and the dry thermometer, when the pressure amounts to thirty inches, is to their difference under any other pressure \( B \), nearly in the inverse ratio of 57 to 27 + \( B \). On this supposition, \( t - e \), the observed depression in the fourth column, before being used in the formula, has been multiplied by \( \frac{27 + B}{57} \); and the difference between the product and \( t - e \) has likewise been applied, with its sign changed, as a correction to \( t \), the temperature of the air. Although the temperature of the moist bulb is the one which is more immediately affected by pressure, it is considered easier to compute a tolerable correction to be applied to the other thermometer, so as still to lead to the same result. Some account of experiments relating to this will be found under the article Evaporation; though, perhaps, owing to the greater dryness and small volume of air operated on, the effect of pressure in most of the experiments there described seems to be greater than in the open air.

A considerable number of experiments on the dew-points corresponding to the indications of the moist and dry thermometers, though only between the temperatures of 69°-5 and 56°-25, are given in the Edinburgh Phil. Jour. for October 1834; but being made under the ordinary pressure, they throw no light on the effects of different pressures; and, considering how little the dew-points go below the temperature of the air, these experiments can scarcely be said to agree so well, either among themselves or with the formula, as the other 15 given above. The author supposes the discrepancies to be owing to the uncertainty attending the use of Daniell's hygrometer, with which they had been observed.

By means of the preceding formula for expressing the relations between the temperatures \( t, e, e' \), the same ingenious author has computed the following table of dew-points, which, however, we have arranged in a more compact form, and curtailed considerably. For since it seems better to leave extreme cases, and such as are of rare occurrence, to be computed by some formula, than to swell out the tables to embrace them, we have omitted all that: ### Table of Dew-Points

| | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | |---|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----| | 1 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | | 2 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | | 3 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | 88 | | 4 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | 87 | | 5 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | | 6 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | 85 | | 7 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | 84 | | 8 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | 83 | | 9 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | | 10 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | 81 | | 11 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | | 12 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | 79 | | 13 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | 78 | | 14 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | 77 | | 15 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | 76 | | 16 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | | 17 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | 74 | | 18 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | 73 | | 19 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | 72 | | 20 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | 71 | | 21 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | | 22 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | 69 | | 23 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | 68 | | 24 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | 67 | | 25 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | 66 | | 26 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | 65 | | 27 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | 64 | | 28 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | 63 | | 29 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | 62 | | 30 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 | 61 |

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**Note:** The table provides dew-point values for various temperatures. It should be noted that the dew-point values are corrected by means of the small table in the lower right-hand corner, which is to be entered at the bottom with the barometric pressure, and on the right side with the observed difference between the wet and dry thermometers. The number thus obtained from this small table is to be subtracted from both arguments of the large table when the pressure falls short of thirty inches, and added when it is greater. A different mode of obtaining from the same data, not only the dew-point, but likewise the force, weight, &c. of moisture in the air, has been proposed by Mr Meikle, in the Edinburgh Phil. Jour. for July 1834 and April 1835, to consist of certain graduated lines or scales delineated on a plane, and are to be used by laying over it any thing most convenient which will form a straight line, such as a common ruler, a thread stretched, &c. This sort of scheme is not deduced from theory, but merely from observation, and seems to admit of being varied very considerably in its form; though it is likely that, when more numerous and certain data have been obtained, some particular modification will be found to have the advantage of the rest.

For we are not aware of any accurate experiments having yet been made on the moist-bulb hygrometer at low temperatures. Plate CCXCVI shows one of the various forms proposed for this purpose in the articles just cited, though it is not here followed up in every particular. The mode of using it will be pretty evident from inspection. If a straight line or ruler be applied to the temperature of the air on the left-hand curve, and at the same time to the temperature of the moist bulb on the oblique straight line, it will both mark the dew-point on the scale so named on the right, and at the same time show on the other scale, a little farther to the right, the weight of moisture actually diffused in a cubic foot of the surrounding air, in grains and tenths of a grain. The like degrees of temperature on the different scales are everywhere disposed in a horizontal straight line. If otherwise arranged, these scales could not be used by simply laying a straight line over them, as is evident if we take a case in which the vapour approaches saturation. The oblique straight line is an asymptote to the two curves nearest it, which are meant for hyperbolas; but the divisions for degrees of temperature decrease a little downward in the lower part of the figure. It has been objected, that the hyperbolas would not suit air absolutely dry, and a dew-point infinitely low; but it is shown at length in the Edinburgh Phil. Jour. for April 1835, that no such case can ever occur in using the moist bulb, and that this scheme is not restricted to hyperbolas. The results obtained by this method sometimes differ considerably at low temperatures from those of the large table of dew-points; but we know of no experiments to decide how far any of them may be right at low temperatures.

We have thought it better at present not to encumber the diagram with what was originally proposed in this scheme as a correction for pressure, because there seems still to be some uncertainty regarding the precise allowance. But when the barometer differs from thirty inches, the approximate correction, which was already noticed above, may be employed here. It is equivalent to using

\[ t + \frac{B + 27}{57} \times (t - t') \]

in place of the actual temperature of the air. The force of vapour corresponding to a known dew-point is sufficiently well ascertained for ordinary purposes; but we have likewise at present omitted the scale proposed for it, in order not to render the scheme too complicated at its first outset. The same allowance for frost will of course be required here as in any other method with the moist-bulb hygrometer.

Were this project fully realized, that is, if by merely laying a ruler across the plate in the manner above mentioned, the dew-point and weight, &c. of the vapour in the air could be indicated at once, and without computation, it would obviously be one of the most convenient methods yet employed for the purpose.

We shall now endeavour briefly to sketch out a few steps towards an investigation of the relation between the dew-point and the corresponding indications of the moist-bulb hygrometer, and have to regret that the present imperfect state of the data does not warrant or enable us to render it more complete. It was shown above, that the value of any particular degree on Fahrenheit's scale of an air-thermometer, that is, the increment or decrement of heat necessary to produce a change of one degree by Fahrenheit's scale, in the temperature of a given mass of air under a constant pressure, will be inversely as the distance of that degree from — 448°. But when the volume and pressure are both constant, with a variable mass, the increment, decrement, or specific heat for one degree of Fahrenheit, will, so far as depends on change of temperature, be inversely as the square of the distance of that degree from — 448°, viz. in the ratio compounded of the mass or density of the air and the value of a degree, each of which varies inversely as the temperature reckoned from — 448. For we have likewise shown above, that the specific heat of a given volume of air is, exteris partibus, as its density. Strictly speaking, it is obviously the fluxion of the heat which varies in this manner. Hence, so far as depends on change of temperature, the fluxion of the quantity of heat in a cubic foot of air cooling under a constant pressure at the temperature \( t \), will be directly as \( dt \), and inversely as \( (t + 448)^2 \). It may therefore be denoted by

\[ \frac{-A \, dt}{(t + 448)^2} \]

where \( A \) is a constant. The fluent of this taken between the temperatures \( t \) and \( t' \) is

\[ \frac{A(t - t')}{(t + 448)(t' + 448)} \]

which is the heat lost by the cubic foot of air while its variable mass is cooling under a constant pressure from \( t \) to \( t' \). Hence, if the specific heat of a cubic foot of dry air of thirty inches pressure, and confined in an inextensible vessel at 32° F. be reckoned unit, and of course only three fourths of what it would be were the pressure constant, the value of \( A \) for the cooling of air under any constant pressure \( B \), must be such that three fourths of it may equal the denominator in the above formula, when \( B = 30 \)

and \( (t + 448)(t' + 448) = (32 + 448)^2 \),

so that, \( A = \frac{3}{4}(480)^2 \times \frac{B}{30} \).

Now, from Dr Haycraft's experiments, it appears that at the same temperature the specific heats of all elastic fluids, and mixtures of them, so far as yet tried, are equal under equal volumes and pressures; and we have shown above, that the specific heat of a cubic foot of air, under a constant pressure, is directly as its density and inversely as its temperature reckoned from — 448°. Combining these together, it follows that the specific heat of a cubic foot of elastic fluid is directly as the pressure and inversely as the square of the temperature reckoned from — 448°; so that, at the same temperature, it is as the pressure simply. It will therefore come to the same thing if, in place of taking the sum of the separate specific heats of air, and of the vapour previously in it, we suppose either to have the joint pressure of both, which will equal that of the atmosphere. Consequently, the heat which a cubic foot of air and vapour at the temperature \( t \) would impart to the wet and colder surface, while cooling through \( t - t' \) degrees, under the constant pressure \( B \), will be

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1 The fluxion of the heat due to the fluxion of the mass, which is the same with the absolute heat in the increment of the mass, is a very different thing, being positive whilst this is negative; nor does it at all pertain to the specific heat. This perhaps would require to be slightly modified, for the mechanical influence of the new vapour which enters into the air during the observation.

We should have been happy to have completed an investigation of the relation between the dew-point and the indications of the moist-bulb hygrometer; but in endeavouring to prosecute it farther, we were met by difficulties which we suspect have been in a great measure overlooked by those who profess to solve the problem with perfect ease. Thus, if we suppose the depressed temperature to extend unaltered to a certain distance from the moist surface, and then all at once to change into the actual atmospheric temperature, is not this to assume an abrupt transition of temperature having no known parallel in nature, especially where the cooling process proceeds so slowly? We cannot comprehend, for instance, how the moist bulb, at a temperature of 70°, could be surrounded by a shell of air also exactly at 70° throughout its whole thickness, while the air immediately outside of this could be at 90°. Nor is there greater probability that the saturated vapour terminates abruptly, or that both terminate exactly at the same distance. Now, if neither the depressed temperature nor the new vapour terminate abruptly or at the same distance, is there anything known of the nature of the law according to which either the one or the other decreases in the actual circumstances? Until some light is thrown on questions like these, everything in the shape of a solution of the problem must rest in a great measure on conjecture; no matter how well successive trials and alterations may bring such an empirical solution apparently to agree with the phenomena. We should think it highly probable that the air enveloping the moist bulb is in a state of continual intermixture similar to that of a fermenting liquor; but how such a state of the air and humidity, if it exist, could be expressed algebraically, we cannot pretend to say.

Another point which, we presume, has not been sufficiently attended to in attempts to solve this problem, is the nature of the latent heat of aqueous vapour, particularly the manner in which it probably varies in different circumstances, and the relation which it bears to its own specific heat and that of air. These we shall now endeavour to examine, in conformity with the foregoing investigation respecting the relations of air to heat, though we can scarcely accomplish this so independently of hypothesis as we did in that case.

When detached from their generating liquids, steam or aqueous vapour, and all elastic fluids yet tried, expand by heat at the same rate as air does, and, like it, observe the law of Boyle, by having the force at the same temperature proportional to the density. But since the second principle above stated regarding the constancy in the ratio of the specific heats, or of $m$ to $n$, seems to be closely connected with the rate of expansion and the law of Boyle, analogy renders it extremely probable that it likewise belongs to all gaseous bodies. Besides, Dr Haycraft's experiments for comparing the specific heats of gases (Edinburgh Phil. Trans., vol. x, p. 195, and Philosoph. Mag. for September 1824, p. 200) afford a farther presumption in favour of this; for they go far to establish as another general law, that under equal volumes, pressures, and temperatures, all elastic fluids have equal specific heats. His apparatus is incomparably the best which, so far as we know, has been applied to the purpose. That of Delaroche and Berard was so unnecessarily complicated, that we cannot adopt their results. Now, from what we have already quoted from Newton (Principia, lib. ii. prop. 23), it readily follows that, if the repulsion between the particles of an elastic fluid vary inversely as any given power of the distance greater than unit, the second principle above mentioned holds respecting that fluid; or its specific heat under a constant pressure exceeds in an invariable ratio its specific heat under a constant volume; and that, if such be the case with steam, the rises of true temperature produced in it by compression must at least be proportional to those in air, whether they may be exactly equal to them or not. This, to be sure, is very different from the theory of Clement, to which we presume, fatal objections have been stated in our article Evaporation (vol. ix. pp. 425, 426). But since there is no known instance of any other law of repulsion than the reciprocal of the square of the distance, it is most unlikely that the particles of air alone should observe this, and other gaseous particles different laws.

From such considerations we are led to conclude that steam should have the ratio of its specific heats not only constant (as Laplace and Poisson maintain), but the same as in air, and consequently have its temperature raised at the same rate by compression; and, till something else be shown to the contrary, we shall adopt Mr Watt's opinion, which, we presume, few will be disposed to dispute, that the latent heat of steam is the same with the heat which would be evolved or rendered sensible by compressing steam to the density of water. By means of these as data we shall proceed to compute the latent heat of steam in terms of its own specific heat. It has been usual to express it in terms of the specific heat of an equal weight of water at some low temperature; as, for instance, to reckon it equal to 1000 times the specific heat of water. This quantity there is reason to suspect to be a very different thing from the sum of the successive specific heats of water, according to the common graduation, continued up through a range of 1000°; in other words, the latent heat of steam is probably very different from the quantity of heat which would raise the temperature of an equal weight of water up through a range of 1000° on Fahrenheit's scale, though they are usually assumed to be equal.

In conformity, then, with the principles which have been laid down as above, let the specific heat of steam at 212°, or the quantity of heat which it would be necessary to add to raise its temperature 1° under a constant volume at 212°, be represented by the variation for one degree in the logarithm of the temperature counted from —448° on Fahrenheit's scale of an air thermometer; namely, by $\log(448 + 213) = \log(448 + 212) = 0.006576$. Steam having a pressure of one atmosphere at 212°, is, according to M. Gay-Lussac, 1694 times rarer than water at 32°, and, consequently, about 1626 times rarer than water at 212°. Hence, on the principles now adopted, were such steam suddenly compressed to the density of water, or to the 1626th part of its bulk, it would have its true temperature raised above 212° by a quantity proportional to, and which might be represented by, $\frac{1}{2} \log_{10}(1626)$; that is, supposing that the specific heat of steam should, like that of air, bear the same ratio to the heat which is evolved or rendered sensible by compression, that 0.006576 bears to $\frac{1}{2} \log_{10}(1626)$ (because $\frac{m-n}{n} = \frac{1}{2}$); and that the heat thus evolved, and which is to raise the temperature of the steam so much under the reduced volume, is equal to the heat which it would have been necessary to have added to the steam before its volume was reduced at all, in order to raise its temperature as much under that original volume unaltered. For we have seen that the magnitude of the volume, if constant, makes no difference on the quantity of heat necessary to raise the temperature of a given mass of air through the same range, and that as little does the intensity of the pressure if constant. Now $\frac{1}{2} \log_{10}(1626) = 1.0703735$, in which 0.006576, the above representa- Hygrometry.

Hygrometric of one degree, is contained 1627-7 times; so that try. 1628° is the latent heat, in terms of the specific heat of the steam itself at 212° under a constant volume. According to MM. Delaroche and Berard, the specific heat of steam, notwithstanding its vastly greater volume, is only 847 of that of water; but since 847 refers to steam under a constant pressure, three fourths of it, or 635, will be the number for steam under a constant volume. Hence the latent heat of steam, in terms of the specific heat of water, should be $1627.7 \times 635 = 1034$, which comes very near the usual estimate; but to this we attach little importance, because we see no ground to believe that the specific heat of steam can be so much, if at all, smaller than that of water at the same temperature. Indeed, considering the vague, complicated, and indirect manner in which Delaroche and Berard obtained the number 847, it is astonishing that other philosophers should ever have adopted it. Were we to suppose the specific heats of steam and water to be equal at 45° (the mean temperature of the water in which Dr Ure condensed the steam in his experiments), the latent heat of steam at 212° would be 1216° in terms of the specific heat of water at 45°, because log. $(448 + 46) - \log.(448 + 45) = 0.0088$, and is contained 1216.3 times in 1.0703735. This, to be sure, rather exceeds the ordinary estimates, which is no great objection to its accuracy; because in the most approved methods hitherto followed for obtaining experimentally the latent heat, there is reason to suspect that some of the steam, in its passage from the boiler or retort, would be so much cooled as to have either attained the liquid form or the state of a cloud before it reached the cold water in which it was to be condensed, a circumstance which would tend to bring out a deficient result, especially if the steam reached the cold water by a horizontal or descending tube, which could not bring back to the boiler any water formed from steam condensed by the way; but it is doubtful if any tube could entirely obviate this, or prevent cloudy vapour from passing over. Besides, the latent heat being generally computed from a slight rise produced by it in the temperature of a large mass of water, it is obvious that a small inaccuracy in measuring such rise may occasion a considerable error in the latent heat; and it has often been alleged that the heat which raises the temperature of water one degree, is far greater than the thousandth part of what would raise it a thousand successive degrees reckoned on the common scale.

But to come nearer our present purpose; since the latent heat of steam, in terms of the specific heat of water, is scarcely a necessary ingredient in the theory of the moist-bulb hygrometer, we shall now compute the latent heat of steam at 32° Fahrenheit, in terms of its own specific heat under a constant volume at that temperature. Steam in a state of saturation at 32° is about 177200 times rarer than water at same temperature, and $\log.(33 + 448) - \log.(32 + 448) = 0.009039$. This, which represents the specific heat, or one degree at 32°, is contained 1935.5 times in 1.74949 = $\frac{1}{2} \log.177200$. Hence the latent heat at 32° is 1935.5. Now, according to the view we have taken of the subject, the latent heat of steam is expressed by the number of times the above numerical value of the specific heat of an equal weight of it at some particular temperature is contained in one third the logarithm of the number of times the steam is rarer than water. But if we wish to express it always in terms of one quantity, as, for instance, in terms of the specific heat of an equal weight of it under a constant volume at 32°, we shall have log. 177200 to log. R. as 1935.5, the latent heat at 32°, to the latent heat of an equal weight of aqueous vapour at a different temperature, and whose rarity, compared with that of water of its own temperature, is R; so that the latent heat, in the terms now specified, will be

$$\frac{1935.5 \log. R}{5.24846} = 368.77 \log. R,$$

which varies as the logarithm of the number of times the steam is rarer than water, as was hinted in the article Evaporation, vol. ix. p. 426. We there noticed, p. 425, an experiment which proves in a very decisive manner, and independently of any thing now stated, that not only the latent, but the total heat in a given mass of steam in a state of saturation must be less at higher temperatures than at lower. Now, both this and the results of our investigation are consistent with, nay afford a very satisfactory reason for, the well-known economy of heat in high-pressure engines; whereas the usually-received theory of Clement, which supposes the latent heat the same at every temperature, is quite incompatible with such economy. Our investigation also leads to a saving of heat in the case of steam used evaporatively, as it is called; but it would here be out of place to go through the computation at length. For some interesting experiments and remarks by Dr Haycraft, on this, which he calls surcharged steam, see Repertory of Patent Inventions, vol. xii. p. 25.

M. de la Rive some time ago proposed for a hygrometer M. de la Rive's following contrivance, which is, in some respects, the Rive's counterpart of the one with the moist bulb. A thermometer being dipped in sulphuric acid, and then exposed to the air, absorbs and condenses the aqueous vapour, which, by evolving its latent heat, and imparting it to the acid, raises the temperature of the thermometer. From this increased temperature, and that of the air, M. de la Rive computes the degree of humidity. In this case, the warming effect of the condensed vapour is restrained by the cooling influence of the air and the radiation of surrounding bodies; whereas in the hygrometer with the moist bulb, the cooling effect of evaporation is limited by the warming influence of the air and radiation. But it is only when the vapour is in a state of half saturation, that either the changes of temperature or the effects of radiation are likely to be nearly equal in the two hygrometers. Perhaps, therefore, a careful comparison of the indications of these instruments in other states of the vapour might afford data for estimating how far they are under the influence of radiation, which would tend materially to elucidate their theories.

While the sulphuric-acid hygrometer displays considerable ingenuity, the other instrument is on several accounts so decidedly preferable, that the invention of M. de la Rive is not likely ever to come into general use. Water can more readily be obtained everywhere, and is much more safe and portable, than sulphuric acid. Besides, owing to sulphuric acid freezing at an uncertain or variable temperature, depending on its strength, such an instrument would be apt to give doubtful results at low temperatures. For, whatever be the strength of the acid at first, it will continue to decrease in an uncertain manner on the bulb by gradually absorbing moisture. However, the heat derived from the condensation of the vapour will sometimes be sufficient to keep the acid in a liquid state at a temperature which would freeze it in a close vessel; and whenever it happens that sulphuric acid remains liquid on the bulb of one thermometer, while water is frozen on that of another, a comparison of the two instruments might throw some light on the influence of frost on the temperature of the latter. We presume, therefore, that the most important use likely to be derived from this hygrometer of M. de la Rive, would be to assist in perfecting the theory of the moist-bulb hygrometer; and possibly some other absorbent substances might answer even better for this purpose than sulphuric acid does.

Since the quantity of aqueous vapour which can exist in Hygro a given volume is independent of the density of the air, it ter by pressi Hygrometry.

It is evident that, when the vapour in the air is in a state of half saturation, we may bring it to complete saturation by injecting additional air into a close vessel till the density is doubled, and doing this either so slowly as not sensibly to warm the air, or to wait a little till the temperature settle. If the vessel is large and of a globular shape, a deposition of moisture should be sensibly produced on its inner surface, so soon as the density gets a very little beyond the double; but with a small vessel, a greater increase of density would be required, because in that case the included mass of vapour would be smaller in proportion to the surface. It would on several accounts be preferable that any vessel for this purpose should be formed of metal with two small openings on opposite sides, closed by bits of glass which would become dim by the deposition of dew on their interior surfaces. Whatever might be the proportion of humidity in the air, it would in all cases be in the inverse ratio of that in which the density was to be increased to produce saturation, and so might be readily had from such a manometer or gauge as is usually employed for showing the pressure, only having a direct place in place of an inverse graduation. If a thermometer were included in the vessel, it would need to be cased like that of Dr Hutton's hygrometer, to protect it from the pressure, which, by compressing the bulb, might cause it to show a temperature far above the truth.

A hygrometer depending on the increase of pressure which additional moisture produces in air not thoroughly damp, will be found described under the article Meteorology; but one depending on the effect which humidity has on the specific gravity of the air might be had by suspending two very light air-tight cylinders of equal dimensions and weight, from the arms of a sensible balance. Thus, if the one cylinder were suspended in a jar containing either a little water, to render the air thoroughly damp, or some drying substance, to render it perfectly dry, the difference in the specific gravities of the exterior and included air would produce a corresponding disturbance in the equilibrium; because the more humid the air, it is the lighter under the same pressure and temperature. The jar would of course need to be closed with a lid, leaving only a small opening for the free motion of a thread or wire suspending the cylinder. The opposite cylinder, too, would need to be suspended in some vessel or cage, only so close as to be a protection from the agitation of the wind.

Since the specific gravity of aqueous vapour is to that of dry air as five to eight, it is evident that when the cylinders, which are to be equal in volume and weight, are both suspended in air of the same temperature and pressure, but differing in humidity, any small weight which being applied to the more buoyant one, would maintain the equilibrium, must be proportional to the difference in the densities of the aqueous vapour surrounding these two opposite cylinders. So that, if the air around the one were made perfectly dry, the requisite counterpoise would just equal three eighths of the weight of as much aqueous vapour as is contained in a volume of air contiguous to the other cylinder, and equal its bulk. This, however, is not meant to apply to fog or cloudy air, nor are we aware that any other hygrometer does apply to fog. But the same result might be had without any counterpoise, by making the arm of the balance show on a graduated arc the disturbance of equilibrium corresponding to such counterpoise. The apparatus now proposed, though it might be somewhat bulky and expensive, would indicate in the most direct manner, and without regard to temperature or pressure, the actual weight of moisture in the air; and might therefore be of great service in trying and verifying other hygrometers, with the view of obtaining the real values of their indications, and perfecting their theories. It would, in short, possess all the properties which Saussure considered essential to a perfect hygrometer.

Having obtained, by means of such an instrument, \( g \) the grains of vapour in a cubic foot of air at the temperature \( t \), the actual force of the vapour will be

\[ f = \frac{t + 448}{565581} \times g. \]

This obviously follows, from what was shown above, in giving the rationale of Leroy's mode of finding the dew-point, namely, that

\[ \frac{30}{212 + 448} \cdot \frac{f}{t + 448} = 257-2188 \cdot g. \]

It was just observed that the density of aqueous vapour is less than that of dry air at the same temperature and pressure, in the ratio of five to eight. Hence, at the same temperature, the specific gravity of a mixture of air and vapour whose tension is \( f \), is to that of dry air under the same pressure \( p \), as \( p - 375f \) to \( p \); and therefore, in the mensuration of heights, the weight of a column of air and moisture will have an effect upon the barometer which, ceteris paribus, will be less than that of an equally long column of the dry air, in the ratio of \( p - 375f \) to \( p \). So that, in conformity with the usual principles on which heights are measured, if \( D \) be the difference in the logarithms of the corrected pressures at the upper and lower stations, \( p \) the mean pressure of the intercepted column of air, \( t \) its mean temperature, and \( f \) the mean force of its vapour, the height in fathoms will be

\[ \frac{p}{p - 375f} \times \frac{t + 448}{480} \times 10000 D. \]

This includes the reduction of the temperature of the air to 32°; because, under the same mean pressure, the weight of the column of dry air at the temperature \( t \) is to its weight at 32° as 480° to \( t + 448 \), which is the well-known rate of the expansion of air. We do not, however, mean, that this or any formula is applicable, when the air happens to be foggy or cloudy. Nor would it be of any use here to speculate on, or to attempt to employ, any law according to which the quantity of aqueous vapour may be supposed to vary at different heights, in the form of an independent atmosphere; because the wind and other uncertain vicissitudes of weather derange every thing of this sort, as is evident from the dew-point being found to vary at different heights in a manner which cannot be referred to any definite law which it might be supposed to have followed in perfectly still air.

From the above investigation, it is evident that under Formula the pressure \( p \) the specific gravity of a mixture of air and for the vapour whose tension is \( f \), will be to that of dry air of thirty inches pressure at same temperature, as \( p - 375f \) to 30. So that, if the specific gravity of the dry air of thirty inches pressure at 32° F. be unit, the specific gravity of the mixture at any temperature \( t \) will be

\[ \frac{p - 375f}{30} \times \frac{480}{t + 448} = \frac{16p - 6f}{t + 448}. \]

Professor Daniell has given, in the second edition of his Essays (p. 177), an extensive table for finding the specific gravity of a mixture of air and vapour, under a pressure of thirty inches, and for facilitating corrections for the effects of vapour and temperature on barometric measurements; but it requires more trouble to apply it to either of these purposes than the preceding formulae do; and it is curious that Mr Daniell does not seem aware that the method he follows for correcting measurements, even when aided by that large table, is only suited to a column of air and vapour in a state of saturation, and Hygrometry—whose mean pressure is exactly thirty inches; though it rarely happens in the measurement of heights, that the mean pressure of the air and vapour forming the column is so great. Thus, the force of vapour in the third column of his table being expressed in terms of a pressure of thirty inches as the unit, can of course suit no other; yet in an example on page 183, he applies it as if the mean pressure, 28-77 inches, had been the unit; and no doubt, when the pressure is smaller, it will lead to a more considerable error. A similar objection attaches to the weight or density of vapour in his fourth column; and besides, when he applies it as the "increase of density for weight of vapour," he uses the density of vapour corresponding to the dew-point, which is always greater than the actual density, except when the vapour is in a state of saturation. It is this step in Mr Daniell's method which restricts it to thoroughly damp air; whereas the formulae we have given above are of general application, only they are not suited to foggy or cloudy air, nor are we aware that any other method is.

We shall now examine some of the more remarkable phenomena resulting from or connected with the deposition of aqueous vapour from the atmosphere. The ingenious Dr James Hutton proposed a theory of rain, which many receive as the true explication of it, viz., that rain is produced by the mixing of different masses of moist air having different temperatures. It is well known from experiment, that the variations in the capacity of air, or more properly of space for moisture, proceed in a higher ratio than the corresponding variations of temperature, as reckoned on the common scales, but still more so with reference to the scale which we deduced above; where it is shown necessarily to follow from admitted principles, that air expands in geometrical progression for equal increments of heat (though this, as we have already noticed, is not precisely the same with the scale which Dr Dalton long ago proposed, and afterwards relinquished). Hence, if the space occupied by the mixture of the different masses of air have either the mean temperature of the whole, or one still lower, its capacity for moisture would come short of the mean, and so a deposition of rain, &c. will ensue, if the air has previously been sufficiently moist. There can be no question that this theory is a possible one; but it would be no easy matter to prove that it is the actual and ordinary mode in which rain is produced. In the Quarterly Journal of Science for April 1829, Mr Meikle adduces some reasons countenanced by experiments, which seem to render it very probable that clouds, rain, &c. may often be traced to a nearer and more natural source. The Huttonian theory does not readily explain why rain is more commonly preceded or attended with a falling barometer; for it is as easy to conceive mixtures of air occurring whilst the barometer rises, as when it falls; and the like objection attaches to the electrical theory of rain. Indeed, on many occasions electricity is as serviceable to the moderns as the occult qualities were to the ancients; for by referring any difficulty to electricity, we can either evade the trouble of solving it, or the mortification of acknowledging our inability to solve it.

But this prognostic of the falling barometer did not long escape notice after the Torricellian experiment had been made; and the explanation then given, and for long after received, was, that the air, from its rarity, was unable to buoy up or support the denser vapours, and so of course down they came. It was not then known, that, at the same temperature and pressure, moist air, especially if transparent, is lighter than dry. Yet the observers of that period certainly inferred, on very probable grounds, that there existed a connection between the concomitant circumstances of decreasing pressure and depositions of rain, &c. from the atmosphere. They are further to be commended in seeking an explanation in a principle which they supposed to be known; because reason and facts are always preferable to hypotheses. We are far from reckoning their statical explanation to have no share in the phenomena; because the denser the air, the more will it retard or obstruct the descent of minute drops of water or particles of snow, &c.; but the suspension of transparent vapour depends on the temperature alone. For it is now well known, as noticed more particularly under the article Evaporation, that the quantity of vapour contained in a given space is independent of the presence or density of any other elastic fluid with which it is not chemically combined; or that the maximum quantity of vapour which can exist in a given space is the same at the same temperature as it would be did that space contain nothing else. Whenever, therefore, the volume of the same mass of air increases, the capacity of that volume for moisture should increase at the same rate, were the temperature to remain the same; but when air dilates from a diminution of pressure, its temperature always falls, if there be no accession of heat from some other source. A fall in the barometer, however, is not necessarily attended with a reduction of temperature near the earth's surface. On the contrary, the temperature there may often be preserved, or even raised (as we shall afterwards explain), by the intermixture of the higher and lower strata, and by the retention of heat, such as had previously escaped upward by radiation from the earth's surface, but which ceases to do so after the sky is obscured by dense clouds. But where none of these extraneous circumstances interfere, the reduction of temperature properly due to dilatation lessens the capacity of the space so cooled for moisture, far more than the enlargement in bulk increases it; so that, generally speaking, if the air be sufficiently moist, a fall in the barometer, or rarefying the air, should tend to produce clouds, rain, &c.

For example, the volume of a given mass of air will increase about a nineteenth part by being raised through a height of a hundred yards; and the capacity of that volume for moisture would increase in the same ratio did

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1 We are aware that some of the first observers are said to have coupled rain with a rising or high barometer; and indeed there are exceptions. When the wind is shifting from west to east, the barometer generally rises, though followed by copious rain; and, on the other hand, when the wind shifts from east to west, the barometer usually falls, though it remains dry. The motion of the barometer is in such cases to a certain extent connected with the earth's diurnal rotation, and is thus accounted for by Mr Meikle, in the Edinburgh Phil. Jour. for December 1827, page 108—"The curvilinear motion of the wind, describing a circle about the earth, in place of always lowering the barometer, as many have supposed, ought frequently to augment the pressure of the atmosphere, and consequently to raise the barometer. At first sight this may seem paradoxical enough, if not thoroughly absurd; but to solve it we have only to consider, that when the wind is from the east, its diurnal motion round the earth's axis is thereby lessened, its centrifugal force will be of course weakened, and so the air will be more at liberty to gravitate or press freely on the earth's surface. Westerly winds, on the contrary, by conspiring with the diurnal motion, increase the centrifugal force, and diminish the pressure."

The influence of centrifugal force on the pressure will likewise afford a satisfactory reason for hills generally measuring higher by the barometer during wind than during a calm; the air being probably accumulated, or the pressure increased, at the bottom of the hill, by the wind describing almost a straight line, or a curve which is convex downward, while the air is dilated or the pressure diminished at the upper station, by the wind describing over the summit a curve which, compared with the other, is very concave downward. But the difference of centrifugal force at the two stations will have little to do with the diurnal rotation, if the wind has the same velocity and direction at both, though the velocity is more likely to be greater at the summit than below. As for the difference of distance from the earth's centre, it is scarcely worth attending to. Hygrometry.

If the temperature continue the same. But if the temperature lost one degree, the capacity for moisture would be thereby diminished about a thirtieth; and therefore, upon the whole, aqueous vapour in a state of saturation would have about its forty-fifth part condensed into water by being raised a hundred yards, namely, a thirtieth minus a ninetieth. However, for reasons given above, and to be further illustrated by and by, it is more likely that the temperature of an ascending current of air will often lose $1^\circ$-5 F. or even more, by gaining an elevation of a hundred yards, which would lessen the capacity for vapour about one twentieth. Hence, a rise of a hundred yards would condense about a twenty-sixth part of the vapour, viz. the excess of a twentieth over a ninetieth.

Such at least would be the result, calculating from the foregoing principles; but the following simple experiment affords a more direct proof that sufficient rarefaction will always change common undried air into a cloud. Connect a small glass flask, containing the ordinary air, with the receiver of an air-pump, by means of an intervening stopcock. Exhaust the receiver with the cock shut; then looking attentively at the flask, open it suddenly into the receiver, by turning the stop-cock, when a momentary mistiness will be perceived in the flask, which is aqueous vapour condensed into a cloud by the cold produced by the rarefaction. The cloud is here formed under peculiar disadvantages, being everywhere surrounded at so short a distance by a warmer surface throwing in heat upon it, and especially by a vitreous surface which is known to radiate powerfully. But a cloud which is visible in so small a volume would be pretty dense on the large scale. We have never tried this experiment without succeeding; but we believe it may fail when the air contains little moisture, if the receiver be not large compared with the flask, or if the connecting stop-cock have a very narrow bore. It is, however, rare for the external air, in a state of free circulation, to contain so little as a third of the total vapour which could exist in it at the actual temperature.

Since both modes of reasoning lead to the same results, we presume enough has now been said to warrant us to conclude, that when air ascends sufficiently in the atmosphere, it must, from being cooled by dilating, constitute a cloud, or, if moist enough, produce rain, &c. For example, if a current of air traverse the ocean till it becomes very moist; and then, if, on arriving at the shore, this current have to rise higher as the land rises, we have at once the reason why rain so frequently commences nearer the sea, and extends thence forward with the wind,—why more elevated situations are more liable to rain,—and why a wind from the land is more rarely attended with rain on its approaching the shore. But there is reason to think that a stream of air which has been gradually elevated by traversing a rising ground, does not always descend again where the surface declines, but, on the contrary, may continue for some time at that height, or, from the upward force it has already acquired, may even rise higher. In this manner it may deposit rain while rolling far above the tranquil plain, as well as when contending with the asperities of the more elevated surface; especially since the humidity, after being condensed, will be borne along with the current, taking some time to force its way down through the air, and the more so as the air is more dense. If the space over which the raining current passes be not saturated with moisture, the air may revaporize a part or the whole of the rain descending in it. This is no doubt the way in which clouds seem suspended in the air, or even at rest in the wind, though, in fact, they may be falling, and changing into transparent vapour, so as to float on unseen in the wind beneath; whilst their place is continually supplied by the successive condensation of other vapour arriving with the current, and which, in its turn, is revaporized or swept away by the wind. Much in the same way clouds are apparently stationed over elevated peaks, or even over large portions of hills; while the fact is, that their particles are moving onward, and others coming in their stead. The apparent motions of clouds may therefore differ so much from the true as to afford a most fallacious measure of the velocity of the wind.

The circumstance of clouds frequenting hills, or apparently moving towards them, will admit of a similar explanation, without the aid of an imaginary force residing in hills for the express purpose of attracting clouds, rain, &c. The notion that mountain-caps, or clouds hovering about the tops of hills, are produced by the cooling influence of the summit, does not appear to be better founded; because such phenomena frequently occur when the air is considerably colder than the surface of the hill, though they may not continue long of very different temperatures. But were the cloud really owing to the colder temperature of the summit, it would not only touch, but be densest next the surface of the hill, wetting it profusely; whereas the cloud is often observed to be several feet, or many yards, clear of the hill, and the surface as dry at least as that of the surrounding country; a clear proof that the hill is not colder than the cloud. A more natural explanation, we presume, is, that the cloud called the mountain-cap is formed in that part of a current of moist air which is sufficiently cooled by the rarefaction attending its sudden increase of elevation in ascending and rolling over the summit; and that this current will regain its transparency so soon as it afterwards passes on to where it either absorbs as much heat, or acquires an increase of pressure sufficient to restore its former temperature. The reason why the cloud is frequently observed to keep clear of the summit for a considerable time, especially during a brisk wind, is, that the centrifugal force due to the curvature of the current over the hill carries it clear of the summit, and the intervening arched space is left to be occupied by comparatively still air, into which the air recently cooled by rarefaction scarcely enters; and by this means the higher temperature of the summit is preserved for some time. In the same way it often happens, that whilst a storm acts with fury on the face of a precipice, a person on the summit only hears the sound, and feels himself as in a calm; the arched current, with its copious load of rain or hail, being carried clear of the summit by the centrifugal force, while the intermediate space is left almost free from wind, hail, or rain. Since caps rarely occur on hills of moderate height, except when the air is pretty moist, they are not unfrequently precursors of rain.

Much in the same way as in the case of the mountain-cap, may the origin of the cloud called the cumulus be traced, especially by means of its horizontal base, to the dilatation of air. Such a cloud may be situated partly in an ascending portion of a current of moist air, and partly in a descending portion; or it may sometimes occupy the most elevated part of an arched-like sweep of the current. Whenever the air reaches the requisite elevation, it will become opaque, but will regain its transparency so soon as it descends again sufficiently to have its temperature restored by increase of pressure. The opacity should terminate underneath nearly all at the same level, or in a horizontal plane, if the heat and moisture have been uniformly or proportionally distributed through the air of the current. When the distribution has been unequal, the base will of course be uneven, or may deviate more or less from a horizontal plane. Perhaps some other modifications of clouds might be accounted for on similar principles. We may farther observe, that clouds, when seen in profile, especially the several parts of the cirrus, when changing into cirro-cumulus, generally appear as if leaning forward like shrubs in the direction in which the wind moves; and longer pieces of cloud are commonly lower in the rear than in front. It is evident that moisture which has ascended in the form of transparent vapour, and descended again as rain, snow, &c., must have left its latent heat above. But much heat no doubt moves upward, from its natural propensity to render the atmosphere of one temperature throughout its whole height, and from the tendency of warmer air to rise above the colder. There is therefore good reason for concluding, that air which has just been suddenly elevated and dilated should be thereby reduced to a much lower temperature than what obtains in air which has remained at that elevation for some considerable time, receiving heat from below, from the sun, or other sources. This is both in accordance with direct observation, and with the conclusions at which we arrived when investigating the relations of air to heat. For the entire fall of temperature properly due to dilatation, as expressed by either of the formulae given above, viz.

\[ (r + 248) \left[ \left( \frac{1}{2} \right)^{\frac{3}{2}} - 1 \right], \text{or} (r + 448) \left[ \left( \frac{1}{2} \right)^{\frac{3}{2}} - 1 \right] \]

far exceeds a reduction of one degree for every 100 yards of ascent. In Gay-Lussac's famous ascent, the pressure was reduced in the ratio of \(432\) to \(1\) at a height of 7600 yards, and the temperature fell \(72^\circ54'\), or from \(87^\circ44'\) to \(14^\circ9'\); so that the density was very nearly halved. With these data, the first formula gives \((87^\circ44' + 448) \left[ \left( \frac{1}{2} \right)^{\frac{3}{2}} - 1 \right] = 110^\circ46'\) for the fall of temperature; but the second gives about \(9^\circ\) less, or \((535^\circ44') \left[ \left( \frac{1}{2} \right)^{\frac{3}{2}} - 1 \right] = 101^\circ35'\); and so it ought, because in Gay-Lussac's ascent the cube of the pressure decreased more slowly than in the ratio of the fourth power of the density. However, there is reason to think that when a strong wind runs up a steep acclivity, the temperature would be found to decrease very nearly in such a manner that the cube of the pressure would, as in these formulas, vary as the fourth power of the density. To make a proper trial of this, it would need to be done on air which is free from any tendency to deposit moisture, as also when the surface of the acclivity is dry, and completely shaded by elevated clouds from the sun and the aspect of a clear sky, in order that the temperature of the air and surface might everywhere correspond. As the wind is more likely to escape past the sides of an elevated peak than go right over its top, an acclivity proper for this purpose would need to be of such an extent that the temperatures and pressures could be observed in parts of the currents where we were sure the air was making no lateral escape. Calculating then from the second formula, it would follow, that when such a current ascends to where the pressure is reduced in the ratio of \(432\) to \(1\), the temperature should fall from \(87^\circ44'\) to \(-18^\circ91'\), or \(101^\circ35'\), which, being greater than \(72^\circ54'\), shows that, in this case, the density would not be reduced quite to the half.

The experiment already described for producing the cloud in the flask shows that if an equal weight of air in the upper regions did not contain far more heat than in the lower, the sky would be perpetually obscured with clouds. This is further illustrated by the circumstance, that when the atmosphere is much agitated and intermixed to a great height, it becomes obscured above, no doubt from the dilatation rendering the recently ascended air colder there than corresponds to the constituent temperature of the vapour which it had brought along with it, while the air beneath, which has recently descended, being warmed to or above the dew-point of its vapour, by compression becomes quite transparent, though previously it might have been opaque. In such cases the clouds often present a deep-blue colour. However, it is long since Dr Dalton (Chemical Philosophy, vol. i. p. 123) proposed the hypothesis that heat was diffused equally, or in the same proportion as the density of the air, throughout the whole height of the atmosphere; in other words, that a given weight of air anywhere in a perpendicular column contained the same quantity of heat. In this he was followed by several eminent philosophers, though it is quite incompatible with the facts now stated, and would, besides, require the temperature to decrease so rapidly with the elevation, that aqueous vapour, by its superior elasticity, would always shoot up through the air to where it would be condensed by the cold into a cloud, keeping the sky perpetually obscured, which is contrary to observation.

It has become a common maxim, that dry air is less transparent than moist; the latter of course being free from fog or cloud. If it is meant that mere dryness impairs the transparency, we should be very apt to question such doctrine, though we do not dispute that the atmosphere is less transparent in very drouthy weather. The reason of this we presume to be, that much solid matter is then diffused through the atmosphere in the form of dust or smoke, a great part of which, had it been sufficiently moist, would have been too heavy to float in the air; and some of the remainder, had it been more humid, might have assumed the gaseous form, so as to be transparent.

The temperature at the tops of mountains is generally found to be lower than that of air at the same height over the plains; and a probable reason for it is, that mountains, besides having their temperatures reduced by radiation, are apt to be further cooled by and enveloped in recently dilated ascending currents of air rolling over them. But here again it should be remembered, that our knowledge of the temperature at great heights over the plains has for the most part been derived from a few ascents in balloons, undertaken during the day, and only in very serene and mild weather, when there was scarcely any interchange going on between the air of the different strata. Nothing is known of the decrease of temperature over the plains in a coarse winter night. The same remarks apply in a great measure to ascents Dare on very high mountains; so that in all probability the mean of decrease of temperature in the atmosphere has hitherto been greatly underrated. Snow-clad mountains are, besides, cooled, particularly in very dry weather, by the evaporation from the snow; and we may remark, by the by, that at the same temperature, dry air is, for the above reason, less efficacious in melting snow than moist. Because the moist air, in place of spending its heat to form vapour, does, in consequence of its touching a colder body, part with a portion of the latent heat of the vapour it already contained, which must greatly aid in liquefying the snow. The melting of snow therefore does not depend solely on the temperature of the wind, but likewise upon its being previously charged with moisture. Besides, when dry air passes over snow on a high mountain, the evaporation, and consequently the reduction of temperature, will be greatly promoted by the diminished pressure which obtains at such heights. This may help to explain why snow-winds, as they are called, should be found so intensely cold; for the mere circumstance of wind having passed over a cold mountain is not a sufficient reason why it should be cold after its descent. But we may here observe by the by, that the reason why snow at great elevations is so little affected by the action of the sun's rays, is, that the rarity of the air induces such a tendency to evaporation, that the moisture evaporates just as fast as it melts, and in this way expends by far the greater part of the sun's heat on the formation of vapour. For since the vaporization of water consumes about seven times as much heat as the melting does, it follows that the heat spent in both melting and evaporating an ounce of snow, would melt no less than eight ounces without evaporation. The explanation which we proposed above of the phenomena of clouds seeming stationary in the wind, appears to be applicable to water-spouts. We readily allow that the ascent of the water in them has been long accounted for in a very rational way, which is briefly this: The collision of currents of air from different quarters produces a whirlwind; the air near the axis of rotation is rarefied by the centrifugal force; and the pressure on the spot under this attenuated air is necessarily diminished. Of course, when a whirlwind occurs on the sea, a lake, or a river, the water rises in the axis of rotation, on the same principle as in the common pump. But the rarefied air itself ascends in virtue of its levity. Its place is supplied by the confluence of the heavier adjacent air, which being rarefied in its turn, ascends; and in this manner an upward current of air is produced, which aids the ascent of the water.

Thus far the explanation is very satisfactory. The other principal part of the phenomenon, the apparent descent of a dense stem from the clouds, nearly over the spot where the water rises, has been ascribed to electricity. But this we cannot help regarding as an evasion savouring of occult qualities, rather than an explanation. It seems nearly allied to the notion that hills attract clouds. The column which apparently descends from the clouds (for any descent is altogether illusory till water actually fall) may be accounted for in the same way as the mountain-cap, viz., that it is aqueous vapour condensed by the cold due to the rarefaction which is occasioned both by the whirling motion of the air and by its rapid ascent. The more swift the rotation, the greater obviously will be the rarefaction and cold; and of course the lower down in the axis or stem will the condensation of moisture extend. The sound and flashes of light seem to be thunder and lightning in miniature, according to a theory which will presently be explained. In attending to this and other atmospherical phenomena, most people are embarrassed with a preconception which is not easily overcome, namely, that clouds are solids, or something more substantial than the air in which they are formed.

We have been long of opinion that the usually received theory of thunder and lightning, as well as that of rain, is unnecessarily complicated and far-fetched, and we therefore regard the following as a more natural and simple one. Volta supposed that bodies, while passing into the gaseous form, absorb electricity, which they emit again on being condensed. Several objections have been made to this, particularly by M. Pouillet; but as they rest in a great measure on the assumption that we possess perfect electrometers, and that experiments made with them are free from every source of fallacy; such objections have not, we think, disproved the more probable opinion of Volta, which has been adopted by several eminent philosophers, who maintain that the electricity emitted by the condensation of steam is always positive. Thunder is unknown in the polar regions, and rarely occurs anywhere in cold weather; from which it appears that thunder does not take place in air incapable of containing much moisture, as is farther confirmed by its being ordinarily produced in a dense cloud. The mode of explaining thunder, &c., which we would therefore prefer, is, that when a large mass of warm and damp air is suddenly moved upwards, it dilates, is cooled, and deposits a considerable share of its moisture, which, in laying aside the gaseous form, parts with positive electricity so suddenly, and in such quantity, that the air is unable to conduct or convey it away in an imperceptible form; and thus the cloud, at the moment of its formation, may in ordinary language be said to emit lightning. The sound may be partly a tremor which the air sustains at the moment the pressure is relaxed by the vapour suddenly losing the elastic form, and may be partly a tremor due to an effort of the electricity to make its escape from the cloud. The thunder and lightning which sometimes attend the condensations of large volumes of steam emitted by volcanoes, are favourable to this theory, as are likewise the noise and lightning of the water-spout already mentioned, if not some parts of the northern lights.

A theory very similar to this, though more in detail, was not long ago proposed to the Royal Society, by the Rev. G. Fisher; but the same thing had been previously suggested by Mr Meikle, in the Quarterly Journal of Science for April 1829.

Several important matters connected with this subject we have not felt warranted to introduce, on account of their not being yet determined by sufficiently extensive observations; such as the maximum, mean, and minimum dew-points for different hours of the day, for different seasons of the year, for different heights in the atmosphere, and in different countries. We now take leave of the subject by referring again to the various works already cited here, and in the article Evaporation; as also to the Reports of the British Association, particularly the very excellent one by Professor Forbes on Meteorology. See also the articles Atmosphere, Aurora-Borealis, Climate, Cloud, Dew, &c. in this work.