The theory of climate, which is commonly treated in a very loose manner, would require much elaborate discussion, and a skilful application of the most refined principles in physical science. But, to form a solid basis for the superstructure, there are still wanted accurate and numerous meteorological facts, which can only be obtained from the diffusion of nice instruments, joined to the zeal of careful observers. We had, besides, expected before this time to have been able to embody the results of some new and delicate researches into the constitution and properties of our atmosphere. Those experiments, however, are not quite completed and brought to their ultimate degree of precision. We must, therefore, content ourselves for the present with tracing the great outlines, reserving the full exposition of the subject to the article Meteorology.

The word Climate, or κλίμα, being derived from the verb κλίνω, to incline, was applied by the ancients, to signify that obliquity of the sphere with respect to the horizon from which results the inequality of day and night. The great astronomer and geographer Ptolemy, distinguished the surface of our globe from the Equator to the Arctic Circle, into climates or parallel zones, corresponding to the successive increase of a quarter of an hour in the length of midsummer-day. Within the tropics, these zones are nearly of equal breadth; but, in the higher latitudes, they contract so much, that it was deemed enough to reckon them by their doubles, answering consequently to intervals of half-an-hour in the extension of the longest day. To compute them is an easy problem in spherical trigonometry. As the sine of the excess of the semidurnal arc above a quadrant is to the radius, so is the tangent of the obliquity of the ecliptic, or of $23^\circ 28'$, to the cotangent of the latitude.

The semidurnal arcs are assumed to be $91^\circ 52'3"$, $93^\circ 45'$, $95^\circ 37\frac{1}{2}'$, $97^\circ 30'$, &c.; and the following table, extracted from Ptolemy's great work, will give some general idea of the distribution of seasons over the surface of our globe:

| Climate, or Parallel | Latitude | Length of Midsummer day | Breadth of Zone | |----------------------|----------|------------------------|----------------| | I | 0° | 12h.00' | 4° 15' | | II | 4° 15' | 12 15 | 4 10 | | III | 8° 25 | 12 30 | 4 5 | | IV | 12° 30 | 12 45 | 3 57 | | V | 16° 27 | 13 00 | 3 47 | | VI | 20° 15 | 13 15 | 3 38 | | VII | 23° 51 | 13 30 | 3 21 | | VIII | 27° 12 | 13 45 | 3 10 | | IX | 30° 22 | 14 00 | 2 56 | | X | 33° 18 | 14 15 | 2 42 | | XI | 36° 00 | 14 30 | 2 35 | | XII | 38° 35 | 14 45 | 2 21 | | XIII | 40° 56 | 15 00 | 2 9 | | XIV | 43° 4 | 15 15 | 1 57 | | XV | 45° 1 | 15 30 | 1 50 | | XVI | 46° 51 | 15 45 | 1 41 | | XVII | 48° 32 | 16 00 | 1 32 | | XVIII | 50° 4 | 16 15 | 1 36 | | XIX | 51° 40 | 16 30 | 1 10 | | XX | 52° 50 | 16 45 | 1 40 | | XXI | 54° 30 | 17 00 | 1 30 | | XXII | 55° 00 | 17 15 | 1 00 | | XXIII | 56° 00 | 17 30 | 1 00 | | XXIV | 57° 00 | 17 45 | 30 | | XXV | 58° 00 | 18 00 | | | XXVI | 59° 30 | 18 30 | | These numbers are calculated on the supposition that the obliquity of the ecliptic was $23^\circ 51' 20''$, to which, according to the theory of Laplace, it must have actually approached in the time of Ptolemy. They seem to be affected by some small errors, especially in the parallels beyond the seventeenth, as the irregular breadth of the zone abundantly shows; but they are, on the whole, more accurate than those given by Varenius.

Ptolemy describes the general appearances which the heavens will present on each parallel, and assigns the corresponding lengths of the shadow of the gnomon at both solstices. He justly maintains, in opposition to the more ancient opinion, that the equatorial region is habitable, since the action of the sun, not continuing long vertical, is there mitigated; but he will not venture to describe the inhabitants, because, no person, he says, having yet penetrated so far south, the reports circulated respecting them appeared to be merely conjectural. He therefore passes over the first parallel to the second.

This second parallel, then, according to Ptolemy, runs through the isle of Taprobana, supposed to be Ceylon, in the latitude of $4^\circ 15'$. The third parallel, in the latitude of $8^\circ 25'$, traverses the gulf of Aulilius. The fourth parallel crosses the Adulitic gulf, in latitude $12^\circ 45'$. The fifth parallel passes through the isle of Meröe, in Upper Egypt, at latitude $16^\circ 27'$. The sixth parallel runs through the territory of the Napati, in latitude $20^\circ 15'$. All these climates or parallels, lying below the tropic, the inhabitants are therefore Amphicians, or see the sun pass twice over their heads in the course of the year. The seventh parallel, at the latitude of $23^\circ 51'$, and consequently bordering the tropic, runs through Syene in Upper Egypt. The eighth parallel, in latitude $27^\circ 12'$, traverses Ptolemais in the Thebaid. The ninth zone, corresponding to a day of $14$ hours of length, passes through Lower Egypt, at the latitude of $36^\circ 12'$. The tenth parallel, in latitude $39^\circ 18'$, runs through the middle of Phoenicia. The eleventh parallel, at the $35^\circ$ degree of latitude, passes through the isle of Rhodes. The twelfth parallel, in latitude $38^\circ 35'$, crosses Smyrna. The thirteenth parallel traverses the Hellespont, in latitude $40^\circ 56'$. The fourteenth parallel, in latitude $43^\circ 4'$, runs through Marseilles. The fifteenth parallel passes through the middle of the Pontic Sea, in latitude $45^\circ 1'$. The sixteenth parallel runs through the sources of the Ister or Danube, in latitude $46^\circ 51'$. The seventeenth parallel, corresponding to a day of $16$ hours in length, traverses the mouths of the Borysthenes, in latitude $48^\circ 32'$. The eighteenth parallel, at the latitude of $50^\circ 4'$, crosses the Palus Mæotis. The nineteenth parallel passes through the most southern part of Britain, in latitude $51^\circ 40'$. The twentieth parallel crosses the mouths of the Rhine, in latitude $52^\circ 50'$. The twenty-first parallel passes through the mouths of the Tanais, in latitude $54^\circ 30'$. The twenty-second parallel, at the $55^\circ$ degree of latitude, traverses the country of the Brigantes in Great Britain, that is, the southern and larger portion of this island, reckoning from the Firth of Forth. The twenty-third parallel, in the $56^\circ$ degree of latitude, passes through the middle of Great Britain. The twenty-fourth parallel, at the latitude of $57^\circ$, runs through Catinactonum in Great Britain. The twenty-fifth parallel, corresponding to a day of $18$ hours long, runs through the southern parts of Little Britain, in latitude $58^\circ$. The twenty-sixth parallel, corresponding to a day of $18\frac{1}{2}$ hours in length, traverses the middle of Little Britain, in latitude $59^\circ 30'$. It should be observed that the latitudes of the places in our own island are most inaccurately given by Ptolemy, and generally advanced about two or three degrees farther north than their true position. By Little Britain, he meant undoubtedly that part of Scotland which lies on the north side of the Firths of Forth and Clyde, and forms almost a peninsula.

The high zones become so narrow, that Ptolemy separates the twenty-sixth to an interval of half instead of a quarter of an hour in the length of the day; but he thinks it superfluous to extend this subdivision farther into such remote and inhospitable countries. Resuming the calculation, however, he places the parallel where midsummer day is prolonged to $19$ hours in the latitude of $61^\circ$, or the north of Little Britain. The parallel of $19\frac{1}{2}$ hours would pass through the Ebudes, or Western Isles, in latitude $62^\circ$. The parallel of $20$ hours runs through the island of Thule, in the latitude of $63^\circ$. The parallel of $21$ hours would traverse the unknown Scythian nations, in latitude $64^\circ$. The parallels of $22$ and $23$ hours would run through the latitudes of $65^\circ$ and $66^\circ$. He places in latitude $66^\circ 8' 40''$ the Arctic Circle itself, where the sun does not set during the whole of midsummer day. Within this circle, the inhabitants are Periscians, or have the sun lingering above the horizon during part of the summer, and the shadow of the gnomon successively projected in every direction. In the latitude of $67^\circ$, the sun continues almost a whole month above the horizon; in the latitude of $69^\circ$, it shines two months; and, in the latitudes of $73^\circ$, $78^\circ$, and $84^\circ$, that luminary displays his presence for three, four, and five months. At the pole itself, the sun appears, during the space of six months, describing circles parallel to the horizon.

its modern acceptation, signifies the peculiar condition of the atmosphere in regard to heat and moisture which prevails in any given place. The diversified character which it displays, has been generally referred to the combined operation of several different causes, which are all reducible, however, to these two—distance from the equator—and height above the level of the sea. Latitude and local elevation form, indeed, the great bases of the law of Climate, and any other modifications have only a partial and very limited influence.

If we dig into the ground, we find the temperature to become gradually more steady, till we reach a tune bale depth of perhaps forty or fifty feet, below which the it continues unchanged. When this perforation is made during winter, the ground gets sensibly warmer till the limit is attained; but, in summer, on the contrary, it grows always colder, till it has gained the same limit. At a certain depth, therefore, under the surface, the temperature of the ground remains quite permanent. Nor is there any indication whatever of the supposed existence of a central fire, since the alleged increase of heat near the bottom of the profoundest excavations is merely accidental, being occasioned by the multitude of burning tapers consumed in conducting the operations of mining. Accordingly, while the air of those confined chambers feels often oppressively warm, the water which flows along the floors seems comparatively cold, or rather preserves the medium heat.

It would be a hasty conclusion, however, to regard this limit of temperature as the natural and absolute heat of our globe. If we dig on the summit of a mountain or any very elevated spot, we shall discover the ground to be considerably colder than in the plain below; or, if we make a similar perforation on the same level, but in a more southern latitude, we shall find greater warmth than before. The heat thus obtained at some moderate depth is hence only the mean result of all the various impressions which the surface of the earth receives from the sun and the atmosphere.

The method employed hitherto for ascertaining the temperature at different depths under ground, consists in digging a hole, and burying a sluggish thermometer for several hours, or the space of a whole night. The celebrated naturalist and accurate observer, Saussure, in the month of October 1785, made an interesting set of observations on the banks of the Arve, near Geneva. By digging downwards on successive days, he reached at last the depth of 31 feet. While the surface of the ground had retained a heat of 60°.3 by Fahrenheit's scale, the temperature of the earth at the depth of 4 feet was 60°.8, at 16 feet 56°, at 21 feet 53°.6, and at 28 feet 51°.8. A thermometer buried 31 feet deep was found, when taken up in summer, to stand at 49°.5; and, when raised in winter, to indicate 52°.2. Notwithstanding this great depth, therefore, it had still felt the vicissitude of the seasons, having varied 2°.7 in the course of the year. The extreme impressions must have taken six months to penetrate to the bulb, since the temperature was lowest in summer and highest in winter.

But this plan of observing is clumsy and imperfect, there not being sufficient time to allow the mass of earth to regain its proper degree of heat, and too much for the instrument to retain its impression unaltered before it can be raised up and observed. In order to throw distinct light on a subject so curious and important, Robert Ferguson, Esq. of Raith, a gentleman whose elegant mind is imbued with the love of science, caused, lately, a series of large mercurial thermometers, with stems of unusual length, to be planted in his spacious garden at Abbotshall, about 50 feet above the level of the sea, and near a mile from the shore of Kirkaldy, in latitude 56° 10'. The main part of each stem having a very narrow bore, had a piece of wider tube joined above it; and to support the internal pressure of the column of mercury, the bulbs were formed of thick cylinders. The instruments, inclosed for protection in wooden cases, were then sunk beside each other to the depths of one, two, four, and eight feet, in a soft gravelly soil, which turns, at four feet below the surface, into quicksand, or a bed of sand and water. These thermometers were carefully observed from time to time by Mr Charles Norval, the very intelligent gardener at Raith; and we have now before us a register of their variations for nearly three years. It thence appears, that, in this climate Depth to and on naked soil, the frost seldom or never penetrates one foot into the ground. The thermometer at that depth fell to 33° of Fahrenheit on the 30th December 1815, and remained at the same point till the 12th February 1816; but, in the ensuing year, it descended no lower than 34°, at which it continued stationary from the 23rd December 1816 to 1st January 1817. At the same depth, of one foot, it reached the maximum 58° on the 13th July 1815, but, in the following year, it rose only to 54°, on the 21st July; and, in the year 1817, it mounted to 56°, about the 5th July. This thermometer, in the space of three years, travelled, therefore, over an interval of 2°, the medium being 45°, and attained its highest and lowest points about three weeks after the solstice of summer and of winter.

The thermometer planted at the depth of two feet, sunk to 36° on the 4th February 1816; but it stood at 38° about the beginning of January 1817. It rose to 56° on the 1st of August 1815; but, in the next year, it reached only 53°, on 24th July; and, in 1817, it again reached 56°, on 10th July. At the depth of two feet, the extreme variation was, therefore, 20°; and the maxima and minima took place about four or five weeks after either solstice.

The thermometer of four feet depth had sunk to 39° about the 11th February 1816; and was stationary at 40°, near the 3d February 1817. It rose to 54°, on the 2d August 1815; and stood at 52° during the greater part of August and September in the years 1816 and 1817. It ranged, therefore, only 15°, the mean being 46°, and the extreme points occurring near two months after either solstice.

The thermometer, whose bulb was planted eight feet deep, descended to 42° on the 16th February 1816, but stood at 42° on the 11th February 1817. It rose to 51° on the 12th September 1815, fell to 50° on the 14th September 1816, and mounted again to 51° on the 20th September 1817. This thermometer had, therefore, a range of only 9°, the medium temperature being 46°, and the extremes of heat and cold occurring nearly three months after the solstice of summer and of winter.

These observations are quite satisfactory, and exhibit very clearly the slow progress by which the impressions of heat or cold penetrate into the ground. It will not be far from the truth to estimate the rate of this penetration at an inch every day. The thermometers hence attained their maximum at different periods, though in a tolerably regular succession. The mean temperature of the ground, however, seemed rather to increase with the depth; but this anomaly has evidently proceeded from the coldness of the two last summers, and particularly that of 1816, which occasioned such late harvests and scanty crops. Thus, the thermometer of one foot indicated the medium heat of only 45°.8 during the whole of the year 1816. But it will be satisfactory to exhibit the leading facts in a tabular form. The following are the mean results for each month, only those for December 1817 are supplied from the corresponding month in 1815: If the thermometers had been sunk considerably deeper, they would, no doubt, have indicated a mean temperature of $47^\circ.7$. Such is the permanent temperature of a copious spring which flows at a short distance, and about the same elevation, from the side of a basaltic or greenstone rock. Profuse fountains and deep wells, which are fed by percolation through the crevices of the strata, furnish the surest and easiest mensuration of the temperature of the earth's crust. The body of water which bursts from the caverns of Vaucluse, and forms almost immediately a respectable and translucent river, has been observed not to vary in its temperature, by the tenth part of a degree, through all the seasons of the year. It is, therefore, an object highly important for scientific travellers, to notice the precise heat of springs in favourable situations, as they issue from their rocky beds. Such choice observations would accurately fix the medium temperature of any climate. It is only requisite to exclude the superficial and the thermal springs, which are not difficult to distinguish.

From a comparison of meteorological observations made at distant points on the surface of our globe, the celebrated Astronomer Professor Mayer of Göttingen, was enabled to discover an empirical law which connects most harmoniously the various results. Round the pole, the mean temperature may be assumed at the precise limit of freezing, since the fields of ice accumulated in that forlorn region seem at this present period neither to increase nor diminish. But under the equator the medium heat on the level of the sea is found to be $84^\circ$ of Fahrenheit, or $29$ centesimal degrees, the division of the thermometric scale which is the best suited to philosophical purposes. At the middle point, or the latitude of $45^\circ$, the temperature is likewise the exact mean, or $144^\circ$ centigrade. From that centre, the heat diminishes rapidly northwards, and increases with equal rapidity towards the south. Hence the mean temperature of any place, at the level of the sea, is calculated in centesimal degrees, by multiplying the square of the cosine of the latitude into the constant number $29$; or it is found by multiplying the supplemental versed sine of double the latitude into $144^\circ$. The variation of temperature for each degree of latitude is hence denoted centesimally, with very great precision, by half the sine of double the latitude; being, in fact, this quantity diminished in the ratio of $58$, the double of $29$, to $57.3$, the length of an arch equal to the radius. From these data, the following table is computed; in which are likewise annexed the corresponding degrees of Fahrenheit's, with the successive differences. | Lat. | Centesimal | Diff. | Fahrenheit | Diff. | |------|------------|-------|------------|-------| | 46 | 13°.99 | .51 | 57°.2 | .92 | | 47 | 13°.49 | .50 | 56°.3 | .91 | | 48 | 12°.98 | .51 | 55°.4 | .91 | | 49 | 12°.48 | .50 | 54°.5 | .90 | | 50 | 11°.98 | .50 | 53°.6 | .90 | | 51 | 11°.49 | .49 | 52°.7 | .89 | | 52 | 10°.99 | .50 | 51°.8 | .90 | | 53 | 10°.50 | .49 | 50°.9 | .88 | | 54 | 10°.02 | .48 | 50°.0 | .87 | | 55 | 9°.54 | .48 | 49°.2 | .86 | | 56 | 9°.07 | .47 | 48°.3 | .85 | | 57 | 8°.60 | .47 | 47°.5 | .84 | | 58 | 8°.14 | .46 | 46°.6 | .83 | | 59 | 7°.69 | .45 | 45°.8 | .81 | | 60 | 7°.25 | .44 | 45°.0 | .79 | | 61 | 6°.82 | .43 | 44°.3 | .78 | | 62 | 6°.39 | .43 | 43°.5 | .77 | | 63 | 5°.98 | .41 | 42°.8 | .76 | | 64 | 5°.57 | .41 | 42°.0 | .74 | | 65 | 5°.18 | .39 | 41°.3 | .71 | | 66 | 4°.80 | .38 | 40°.6 | .68 | | 67 | 4°.43 | .37 | 40°.0 | .67 | | 68 | 4°.07 | .36 | 39°.3 | .65 | | 69 | 3°.72 | .35 | 38°.7 | .63 | | 70 | 3°.39 | .33 | 38°.1 | .60 | | 71 | 3°.07 | .32 | 37°.5 | .57 | | 72 | 2°.77 | .30 | 37°.0 | .54 | | 73 | 2°.48 | .29 | 36°.5 | .52 | | 74 | 2°.20 | .28 | 36°.0 | .50 | | 75 | 1°.94 | .26 | 35°.5 | .47 | | 76 | 1°.70 | .24 | 35°.1 | .43 | | 77 | 1°.47 | .23 | 34°.6 | .41 | | 78 | 1°.25 | .22 | 34°.2 | .40 | | 79 | 1°.05 | .20 | 33°.9 | .36 | | 80 | .86 | .19 | 33°.6 | .34 | | 81 | .71 | .17 | 33°.3 | .31 | | 82 | .56 | .15 | 33°.0 | .27 | | 83 | .43 | .13 | 32°.8 | .23 | | 84 | .32 | .11 | 32°.6 | .20 | | 85 | .22 | .10 | 32°.4 | .18 | | 86 | .14 | .08 | 32°.3 | .15 | | 87 | .08 | .06 | 32°.2 | .11 | | 88 | .04 | .04 | 32.1 | .07 | | 89 | .01 | .03 | 32.0 | .05 | | 90 | .00 | .00 | 32.0 | .01 |

It hence appears, that, near the extremities of the quadrant, or towards the pole and the equator, there is scarcely any sensible variation of the mean temperature, and that the whole change within the arctic circle, or between the tropics, amounts only to 8 degrees on Fahrenheit's scale. Very little increase of heat is, therefore, observed in advancing through the torrid zone to the equator; and the intensity of the cold would not be sensibly augmented in penetrating from the arctic circle to the pole. The existence of an open sea towards the extreme north is hence not improbable.

On the other hand, the character of the climate changes rapidly in the temperate zone. Hence likewise the variety of vegetable productions with which those happier regions abound. Such a country as of Temperate France, for example, stretching from about the 40th degree in the to the 50th degree of latitude, and through a difference of five centesimal degrees of mean temperature, yields not only plentiful crops of wheat, barley, and oats, but raises olives, fig-trees, and vines.

The gradation of temperature in different latitudes may be clearly shown by a geometrical diagram. Let the figure below represent a quadrant, 90° the pole, and 50° the latitude of any place; on the radius as an axis and a parameter, describe a parabola, which will consequently pass through the pole; draw the perpendicular 50 B, and the portion of it AB, intercepted within the parabola, will express the mean temperature of the given place at the level of the sea, which in the present case should amount to 12 centesimal degrees.

Since each elementary zone of the sphere is equal to the corresponding belt of a circumscribed cylinder, the whole heat accumulated on its surface must be proportional to the area of the annexed parabola, and, consequently, the mean temperature is two-thirds of what obtains at the equator, and, therefore, 193° or 66° 8' on Fahrenheit's scale. Such must be the temperature of the great mass of the earth, if it has derived all its heat from external impressions. But, at the very small depths to which we can ever penetrate, the influence of the immediate vicinity only is felt; nor, in the profoundest mines, has any tendency been yet perceived towards increase of temperature in the higher latitudes, or of decrease in the lower.

These superficial impressions are all produced either directly, or through the intervention of the atmosphere, by the action of the solar rays. It may be calculated from experiment, that the entire and unimpaired light of a vertical sun will communicate one centesimal degree of heat every hour to a sheet of water of a foot in thickness. Consequently, since the surface of a sphere is four times that of its generating circle, such a sheet of water, spread over the whole of the globe, would receive six degrees of heat every day. But the very inferior capacity of the atmosphere for heat, being estimated as equal to that of a body of water about 12 feet in depth, if the aerial mass finally received and retained all the calorific impressions, it would every day have its temperature raised half a degree, and, therefore, augmented to $182^\circ$ in the course of a whole year. This annual accession of heat, however, is quickly dispersed by the mobility of the fluid medium, and gradually absorbed into the earth, or more quickly diffused through the waters of the ocean, which, besides, occupy at least three-fourths of the whole surface of our globe. The luminous matter, communicated by the incessant shining of the sun, whether received on the ground, or intercepted in its passage through the air, would hence be capable of communicating one centesimal degree of heat to the body or the earth in the space of 1323 years; a quantity too small, perhaps, to be yet perceived, though its influence may be afterwards detected by very delicate observations.

It is easy to demonstrate, from the laws of optics, that the quantity of light which falls on a horizontal surface must be proportional to the sine of its obliquity. Hence the aggregate light received under the equator at either equinox, is to what would accumulate during twenty-four hours, if maintained at its highest intensity, as the diameter to the circumference of a circle. This daily accession of heat, confined to the mass of atmosphere, would, therefore, in that climate and season, amount to 633 thousand parts of a degree. At the pole itself, during the complete circuit of the sun in midsummer's day, the measure of heat would be about a fourth part greater, or 797 thousand parts; the continued endurance of the sun above the horizon more than compensating for the feebleness of his oblique rays.

In general, the quantity of light received at any place from the sun in the space of one day is denoted by the product of the sine of the semidurnal arc, or the distance from noon to the time of sunsetting, into the cosines of the latitude and declination, joined to the product of that arc itself into the sines of the latitude and declination; the latter part of the expression being considered as additive or subtractive, according as the declination lies on the same or on the opposite side of the latitude. Hence, at Edinburgh, in the latitude of $56^\circ$, the heat collected during one day at the summer solstice is 307 thousand parts, but at the solstice of winter only 166.

If a calculation be instituted for the quantities of heat during the half yearly periods, from the equinox of spring to that of autumn, and from the autumnal equinox again to the vernal, the following table will be formed.

| | Summer | Winter | Whole Year | |----------------|--------|--------|------------| | Equator | $116^\circ$ | $116^\circ$ | $232^\circ$ | | Tropic | $127$ | $87$ | $214$ | | Latitude $45^\circ$ | $120$ | $42$ | $162$ | | Arctic circle | $102$ | $12$ | $114$ | | Pole | $84$ | $00$ | $84$ |

The annual accumulation at the latitude of $45^\circ$ is thus $162^\circ$, which differs very little from $158^\circ$, the mean between the calorific effects at the equator and at the pole. It may be observed likewise, that the effects vary more slowly at the extremes than near the middle of the quadrant. Thus, from the equator to the tropic, and from the arctic circle to the pole, the differences are $30^\circ$ and $28^\circ$; but in the narrower intervals, from the tropic to the latitude of $45^\circ$, and thence to the arctic circle, the differences are $52^\circ$ and $48^\circ$. The property now stated corresponds with the changes of mean temperature in different latitudes.

If a current of air from the equator, having the ordinary temperature of $29^\circ$, were supposed to travel to the pole, from which an equal and contrary current would consequently flow towards the equator, each journey would transport $58$ degrees of heat. Between two and three such journeys performed every year, would therefore be sufficient to disperse the whole accumulation of $148^\circ$. This only requires the existence of a wind advancing northwards at the rate of 46 miles every day. It is not necessary even that the wind should either continue permanent, or blow directly north. The same effect would be produced, if it were to blow indifferently to every point of the compass, and only at the rate of three miles an hour; a supposition which agrees perfectly with actual observation.

The circulation excited in the body of our atmosphere thus prevents the heat shed by the sun on different parts of the earth's surface from an excessive accumulation. In proportion as the equatorial regions grew warmer from the predominance of illumination, the polar wind would rush with more rapidity, till it had tempered the excess. This balance of the accession, and the consequent dispersion, of heat, has probably been long attained, and it now regulates the gradation of climates in successive latitudes. But if air had possessed the capacity for heat which belongs to hydrogen gas, it would have produced a more equable diffusion of temperature, insomuch that the temperature of the equator could not have become ten degrees warmer than that of the poles. On the contrary, had our atmosphere been less fluid, or less capable of containing heat, the inequality of different climates would have risen to a higher pitch. That variety of temperature which occurs at present on the surface of the globe, was requisite for the development of the different vegetable tribes which clothe it. The same harmony connects the system of this lower world which irradiates the expanse of the celestial regions.

The equilibrium of temperature preserved over the globe by the circulation of the atmosphere, is not, however, very quickly produced. Hence the remarkable increase of heat which takes place during the summer months in the higher latitudes. But within the arctic circle, another powerful agent of Nature, is constantly tempering the inequality of the seasons. The vast beds of snow or fields of ice which cover the land and the sea in those dreary retreats, absorb, in the act of thawing or passing again to the liquid form, all the surplus heat collected during the continuance of a nightless summer. The rigour of winter, when darkness resumes her tedious reign, is likewise mitigated by the warmth Of the light received from the sun, which, by its union with other bodies, constitutes heat, a considerable portion is always detained and absorbed, in its passage through the atmosphere. Even a vertical ray shot through the clearest air, will lose more than the fifth part of its intensity, before it reaches the surface of the earth. In most cases, the loss which light will suffer in the shortest transit through the atmosphere, may be estimated at one fourth of the whole. But the oblique rays must undergo a much greater absorption. If, from their slanting course, they have to encounter twice the number of aerial particles, their intensity must be reduced to nine-sixteenths or the square of three-fourths; and if they describe triple the vertical tract, only twenty-seven sixty-fourth parts, or the cube of three-fourths, will reach the ground. In general, if the tracts of light follow an arithmetical progression, the diminished force with which it escapes and arrives at the ground, will form a decreasing geometrical one. To determine the train of aerial particles which the oblique rays of the sun must traverse in their passage through the atmosphere, is a nice problem, which requires a skilful application of the integral calculus.

Without stopping to engage, at present, in the details of this intricate investigation, it may suffice to remark, that, in general, the length of the tract is nearly in the inverse ratio of the sine of the sun's altitude. But the following table, to every five degrees, is calculated from rigorous formulae; the length of oblique tract being reduced to the same standard of air uniformly dense. These quantities again are diminished in the ratio of the sine of obliquity, to express the calorific action which those enfeebled and slanting rays finally exert at the surface of the earth.

| Sun's Altitude | Measure of Atmospheric Tract | Intensity of the Light Transmitted | Calorific Action at the Surface | |---------------|-----------------------------|-----------------------------------|-------------------------------| | 90° | 1.000 | .750 | .740 | | 85 | 1.004 | .749 | .747 | | 80 | 1.015 | .747 | .735 | | 75 | 1.035 | .742 | .717 | | 70 | 1.064 | .736 | .691 | | 65 | 1.103 | .728 | .660 | | 60 | 1.154 | .718 | .609 | | 55 | 1.220 | .704 | .577 | | 50 | 1.305 | .687 | .526 | | 45 | 1.413 | .666 | .454 | | 40 | 1.554 | .640 | .411 | | 35 | 1.740 | .606 | .348 | | 30 | 1.995 | .563 | .282 | | 25 | 2.359 | .507 | .214 | | 20 | 2.905 | .434 | .148 | | 15 | 3.841 | .331 | .086 | | 10 | 5.610 | .199 | .035 | | 5 | 10.450 | .050 | .004 | | 0 | 37.850 | .00002 | |

It hence appears that, even when the sky is most serene, only one-half of the sun's light can reach the surface of the earth from an altitude of 25°, or one-third from that of 15°, and that, if the obliquity of the rays were increased to 5°, no more than the twentieth part of them would actually be transmitted. The annual quantity of light which falls may be computed as equivalent at the equator to an uniform illumination from an altitude of 17° 46′; and, in the mean latitude of 45° and at the pole, the effects are the same as if the rays had respectively the constant obliques of 13° 2′ and 7° 17′. Therefore, under the most favourable circumstances, of 1000 parts of light transmitted from the sun, only 378 can, at a medium estimate, penetrate to the surface at the equator, 228 in the latitude of 45°, and 110 at the pole of their oblique rays; but the shades received by a given portion of the surface are still less, being only 115, 51, and 14. In cloudy weather, the portion of light that can finally reach the ground will seldom amount to the third of these quantities; and when the sky becomes darkened with accumulated vapours, almost every shining ray is intercepted in its passage.

The light which at last gains the surface being there absorbed and converted into heat, is, in this form, profusely delivered to the ambient air, or more feebly conducted downwards into the body of the earth. But the rays which fall on seas or lakes are not immediately arrested in their course; they penetrate always with diminishing energy, till, at a certain depth, they are no longer visible. This depth depends, without doubt, on the clearness of the medium, though probably not one tenth part of the incident light can advance five fathoms in most translucent water. The surface of the ocean is not, therefore, like that of the land, heated by the direct action of the sun during the day, since his rays are not intercepted at their entrance, but suffered partially to descend into the mass, and to waste their calorific power on a liquid stratum of ten or twelve feet in thickness.

But the surface of deep collections of water is kept always warmer than the ordinary standard of the place, by the operation of another cause, arising from the peculiar constitution of fluids. Although these are capable, like solids, of conducting heat slowly through their mass, yet they transfer it principally in a copious flow by their internal mobility. The heated portions of a fluid being dilated, must continue to float on the surface; while the portions which are cooled, becoming consequently denser, will sink downwards by their superior gravity. Hence the bed of a very deep pool is always excessively cold, since the atmospheric influences are modified in their effects by the laws of statics. The mean temperature of the climate is not communicated by those variable impressions; every change to warmth being spent on the upper stratum, while every transition to cold penetrates to the bottom, which thus experiences all the rigours of winter, without receiving any share of the summer's heat. But, if the beds of profound bodies of water remain perpetually cold, their surface undergoes some variety of temperature, and is generally warmer than the average weekly or monthly heat of the air.

These principles are confirmed by observations made on our own lakes, and strikingly exemplified in those of Switzerland, which have a breadth proportioned to the stupendous altitude of their circling mountains. It appears, from the careful observations of Saussure, that the bottoms of those majestic basins, whether situate in the lower plains, or embosomed in the regions of the upper Alps, are almost all of them equally cold, being only a few degrees above the point of congelation. That accurate observer found the temperature of the Lake of Geneva, at the depth of 1000 feet, to be $42^\circ$, and could discover no monthly variation under 160 feet from the surface. In the course of July, he examined the Lakes of Thun and Lucerne; the former at the depth of 370, and the latter at that of 640 feet, had both the temperature of $41^\circ$, while the superficial waters indicated respectively $64^\circ$ and $68^\circ$, by Fahrenheit's scale. The bottom of the Lago Maggiore, on the Italian side of the Alps, was a little warmer, being $44^\circ$ at the depth of 360 feet, while the surface was almost as high as $78^\circ$. Barlocchi has since found that the Lago Sabatino, near Rome, at the depth of 490 feet, was only $44^\circ$, while the thermometer, dipped at the surface, marked $77^\circ$.

Through the friendship of Mr James Jardine, Civil Engineer, we are enabled to give the results of his observations on some of the principal Scottish lakes, which, as might be expected from him, were conducted with the most scrupulous accuracy. The instrument which he employed for exploring the temperature at different depths, was free from the ordinary objections; being a register thermometer, let down in a horizontal position, which could acquire the impression in not many seconds, and might be drawn up leisurely, without risk of subsequent alteration. It would appear, that the variable impressions of the seasons do not penetrate more than 15 or 20 fathoms; that, below this depth, an almost uniform coldness prevails. Thus, in the deepest part of Loch Lomond, on the 8th September 1812, the temperature of the surface was $59^\circ$ of Fahrenheit; at the depth of 15 fathoms $45^\circ$; at that of 40 fathoms $41^\circ$; and, from that point, to about 3 feet from the bottom, at 100 fathoms, it decreased only the fifth part of a degree. Again, on the preceding day, the superficial water of Loch Katarine being at $57^\circ$, the thermometer, let down 10 fathoms, indicated $50^\circ$; at the depth of 20 fathoms it marked $43^\circ$; at the depth of 35 fathoms it fell to $41^\circ$; and on the verge of the bottom, at 80 fathoms, it had only varied to $41^\circ$. At the same place, on the 3d September 1814, the heat of the surface was $56^\circ$; at the depth of 10 fathoms $49^\circ$; at that of 20 fathoms $44^\circ$; at that of 50 fathoms $41^\circ$; and at that of 80 fathoms $41^\circ$.

Hence it is that, even in the northern latitudes, the deep lakes are never, during the hardest winters, completely frozen over. But if the same water be let into a shallow basin, it will, in a rigorous season, be chilled thoroughly, and converted into ice. This may even happen when spread above the surface of salt water, which is always considerably denser. Thus, frost takes no effect on Loch Ness, nor on the river of that name, which, in a rapid course of a few miles, discharges the surplus water into the sea. But in very severe winters, a sheet of ice appears formed along the shore; the impressions of cold being almost wholly expended on the accumulation of fresh water, since the chilled portions of this which continually descend are stopped in their progress by the greater density of the recumbent sea water.

The seas and the ocean itself obey the same law of the distribution of heat; only the difference of temperature experienced by sounding in the Mediterranean is less conspicuous than in the fresh-water lakes. Saussure found the temperature at the bottom, in the Gulfs of Nice and of Genoa, at the depths of 925 and of 1920 feet, was the same, or $55^\circ$, the heat of the superficial water being about $60^\circ$. But the mean temperature, or that of the body of the land on the same parallel of latitude, is $59^\circ$. The smallness of the diminution here observed may perhaps be attributed to the effect of evaporation in such hot confined bays, the water at the surface being thus rendered saltier, and consequently disposed, by its acquired density, to sink into the colder mass below.

In open seas, and in damper climates, the depression of temperature is greater in the inferior strata. This difference becomes augmented in proportion of the extreme variation of the seasons. Lord Mulgrave, on the 4th September 1773, in the latitude of $65^\circ$ north, drew up water from the depth of 4100 feet, which he found to have the temperature of $40^\circ$, while the thermometer, dipped at the surface, stood, on the 19th June, at $55^\circ$. In the latitude of $66^\circ$, a register thermometer, let down 4680 feet, marked $26^\circ$, while the air was at $48^\circ$; and on the 31st August, in the latitude of $69^\circ$, while the exterior thermometer indicated $59^\circ$, the temperature of the water at the depth of 4040 feet was only $32^\circ$. In shallow seas, the two extremes are brought closer together, and therefore a similar difference of temperature now occurs at moderate depths. The water lying on the surface, which, in the vicissitude of the season, comes to be chilled, is not precipitated as before to a fathomless abyss. The increase of cold below is hence considered as an indication of the proximity of banks, if not of the approach to land itself.

A like gradation of temperature is produced by the alternating influence of the seasons in deep and stagnant masses of air. When this active fluid is confined in profound caverns, opening to the sky without being much exposed, and either perpendicular or gently inclined, its lower strata become intensely and permanently cold. The mild air of summer floats motionless at the mouth of the pit; but, in winter, the superior air, cooled many degrees perhaps below the freezing point, and therefore greatly condensed, precipitates itself continually to the bottom.

This fact takes place in most caverns, and in draw-wells which are left uncovered. Saussure found, on the first of July, when the thermometer in the shade stood at $78^\circ$ of Fahrenheit, that a cave in the Monte Testaceo, a small hill in the vicinity of Rome, formed entirely by the enormous accumulation of broken pottery, had the temperature of $50^\circ$; and two other caves in the same porous mass cooled to $44^\circ$. On the 9th July, when the external air was at $61^\circ$, the cave of St Marino, at the foot of a sandstone hill, about 2080 feet above the level of the sea, indicated only $44^\circ$. which is 8° degrees below the mean temperature of the soil in that situation. In the grotto of Ischia, and in the caves of Cesi and of Chiavenna, the thermometer marked likewise 44°; but, in the caves of Caprino, on the borders of the Lake of Lugano, it stood at different times of the year at 37°, and at 42°; and in those of Hergisweil, near Lucerne, the heat of the interior, on the 31st of July, was only 39°.

But this phenomenon is still more striking in certain peculiar circumstances. The famous Swedish mine of Dannemora, which yields the richest iron ore in the world, presents an immense excavation, probably two or three hundred feet in depth. On the occasion of some repairs, which suspended the usual labours, the basin appeared some years since full of water, with huge blocks of ice floating in it.—The silver mine of Kongsberg in Norway has for its main shaft a frightful open cavern, perhaps three hundred feet deep, and thirty feet wide, of which the bottom is covered with perpetual snow.—Hence, likewise, on the sides of Ætna and of the mountains in Spain, the collected snows are preserved all the year in caves and crevices of the rocks, from which natural stores the muleteers carry down, during summer, to the villages and the cities of the plain, a material so necessary to comfort in those parched climates.

Such is the disposition induced in a confined column of air; but, in a free atmosphere, the gradation of temperature is exactly reversed, the lower strata being invariably warmer than the upper. This most important fact in meteorology and physical geography was thought sufficiently explained in the infancy of physical science, from the proximity of the heat supposed to be reflected by the surface of the earth. But it were idle to attempt any serious confutation of such crude ideas. The true cause of the cold that prevails in the higher regions of the atmosphere, is undoubtedly the enlarged capacity which air acquires by rarefaction. From the unequal action of the sun's rays, and the vicissitudes of day and night, a quick and perpetual circulation is maintained between the lower and the upper strata; and it is obvious that, for each portion of air which rises from the surface, an equal and corresponding portion must likewise descend. But that which mounts up, acquiring an augmented attraction for heat, has its temperature proportionally diminished; while the correlative mass falling down, carries its share of heat along with it, and again relaxing its attraction, seems to diffuse warmth below. A stratum at any given height in the atmosphere is hence affected both by the passage of air from below and by the return of air from above, the former absorbing a portion of heat and the latter evolving it. But the mean temperature at every elevation is on the whole still permanent, and, consequently, those disturbing causes must be exactly balanced, or the absolute measure of heat is the same at all heights, suffering merely some external modification from the difference of capacity in the several portions of the fluid with which it has combined. That temperature is hence inversely as the capacity of air having the rarity due to the given altitude.

It only remains, therefore, to discover the capacity of air, or its attraction for heat under successive pressures, or at different degrees of rarity. But this problem requires a very nice investigation, and appears incapable of being resolved by any direct procedure. If the elaborate experiments of Dr. Crawford and others on the capacity of air in its ordinary state, gave such erroneous results, what hope could be formed of ascertaining even its minute shadings by any similar plan of operation? Fortunately, independent almost of any theory, a simple method occurs for conducting this research. A delicate thermometer, suspended within the receiver of an air-pump, indicates a decrease of temperature, as the process of rarefaction advances. But, on stopping this operation at any stage, the thermometer will slowly regain its former state. If now, when the equilibrium is restored, the air be suddenly re-admitted, the dilated portion which had remained in the receiver, liberates the heat absorbed by it during the progress of rarefaction. The thermometer, accordingly, rises quickly through a certain space, then becomes, for a short while, stationary, and afterwards slowly subsides. But the instrument does evidently not measure the whole of the heat thus evolved, a great part of it being spent in warming up to the same point the internal surface of the receiver. This action, however, is merely superficial, since its effect appears to be momentary. Consequently, the internal surface of the receiver, with that of the plate on which it stands, as penetrated by the sudden impression to a certain very minute depth, forms a constant film of matter, which, as well as the body of air itself, draws its supply from the extricated heat. Under the same receiver, therefore, although the air will not seize the whole of the heat disengaged in the act of admission, it must always retain a proportional share of it. A series of experiments, at successive degrees of rarefaction, must hence discover, if not the absolute, yet the relative, changes of the air's capacity for heat.

To institute this inquiry with the desired success, Details of an excellent and powerful air-pump was used, having the Experiment a receiver of the very largest dimensions, of an oblong spheroidal form, approaching, however, nearly to the globular, and with a narrow bottom. The apparatus being placed in the middle of a close room, which had a steady temperature, a thermometer with a slender stem, open at top, and a small bulb of extreme sensibility, was fixed in a vertical position, a few inches above the centre of the plate. Having replaced the receiver, and allowed it to stand some time, one-fifth of the air was now extracted from under it; and, after a considerable interval, the cock was suddenly opened, to restore the equilibrium; and the mercury of the thermometer, which had been stationary, mounted up very rapidly 3.0 centesimal degrees, from which point it afterwards slowly descended.

The temperature of the room having been regained, two-fifths of the air in the receiver was then extracted; and, after some lapse of time, the external communication being repeated, the thermometer rose instantly 5.3 centesimal degrees. On extracting three-fifths of the internal air, the corresponding ascent of the thermometer, at the restoration of the equilibrium, was 7.0 of those degrees; and, when the contents of the receiver had been rarefied five times, the heat evolved, on the re-admission of the air, amounted to 8.0 degrees. The rate of progressive effect was thus evidently diminishing. On pushing the rarefaction as far as it was really practicable, or till the residual air had become rarefied about 300 times, the change indicated by the thermometer did not reach to more than 8.3.

But, to determine the absolute quantity of heat which is disengaged in the transition of air from a rarer to a denser state, it becomes necessary to ascertain what part of it was consumed on the sides of the receiver. By varying the size of the receiver, and consequently altering the proportion between its surface and its contents, some light may be thrown on this question. Another similar receiver was therefore provided, having half the former dimensions; and with this the same set of experiments was repeated. Its included air being reduced successively to the density of four-fifths, three-fifths, two-fifths, and one-fifth, and then rarefied as much as possible, the thermometer mounted each time through the shorter spaces of 1.8, 3.2, 4.2, 4.8, and finally 5.0 centesimal degrees. These quantities evidently follow the same proportion as the former, of which indeed they are only three-fifths. But the smaller receiver, having, under the fourth part of the surface of the larger, only the eighth part of its contents, exposes comparatively twice the extent of surface. The rise of temperature which its included air exhibits, must consequently be the same as what would have obtained within the larger receiver, if, while its capacity remained the same, its surface had been actually doubled. If we suppose the air to hold one part of the heat, while two parts and four parts are respectively expended on the inside of the receivers, the results would correspond with observation; for the whole quantity evolved, being in both cases the same, the air under the larger receiver would retain one-third, and, under the smaller receiver, only one-fifth; the impressions being thus in the ratio of five to three. The same conclusion may be obtained somewhat differently. If the heat spent on the inside of the large receiver had been spread over twice the surface, it would have raised the temperature only 1°.5; but this mounted really to 1°.8, and therefore the difference .3 was the effects of 1°.8, derived from the contained air. Of the heat thus shared between the air and the doubled surface, one part was hence retained, and five communicated. Consequently, to obtain the true results, it is only necessary to multiply the second set of quantities by five, or the first set by three. If no waste, therefore, took place against the inside of the receiver, the heat evolved in the passage of air from the densities of four-fifths, three-fifths, two-fifths, one-fifth, and extreme rarefaction, to its ordinary state, would be 9, 16, 21, 24, and 25 centesimal degrees.

It is not difficult to discover the law of this progression. They are obviously formed by the successive addition of the odd numbers 9, 7, 5, 3, and 1; and are, consequently, the excesses of the square of 5 above the squares of 4, 3, 2, and 1. Therefore, if the square of the density be taken from unit, the remainder, multiplied by 25, will express in centesimal degrees, the rise of temperature which accompanies the return of the air to its ordinary state.

The numbers thus obtained, however, do not still express the final results. If the restoration of four parts of the air included under the receiver to their usual density, disengage heat, sufficient to raise the temperature of the whole five parts 9 degrees, its real measure must have been 11.5 degrees, or the former augmented in the ratio of 4 to 5. For the same reason, if three-fifths, two-fifths, and one-fifth of the air in the transition of density, evolve portions of heat, which would elevate the temperature of the mass 16, 21, and 24 degrees, the actual quantities are 26°, 52°, and 120°, or those numbers multiplied by 5, and divided by 3, 2, and 1.

These conclusions are easily reduced to formulae. Let $\theta$ denote the density of the air, and $25 \left(1 - \frac{\theta^2}{\theta}\right)$ will express, in centesimal degrees, the elevation of the thermometer which would follow the readmission of the air, if none of the heat were spent on the inside of the receiver. Consequently, $25 \left(\frac{1}{\theta} - \theta\right)$, or $25 \left(\frac{1}{\theta} - \theta\right)$, will exhibit, on the same scale, the whole quantity of heat evolved in the restoration of density. The last formula is extremely simple, implying that 25, multiplied into the difference between the density of air and its reciprocal, will represent the measure of heat due to the change of condition. This result may be either additive or subtractive; it may express the heat emitted in the condensation of air, or the heat absorbed during its opposite rarefaction.

Thus, the heat extricated from air which has its density doubled is $25 \left(\frac{1}{2} - \frac{1}{2}\right)$, or 37°; and the same quantity is withdrawn, either when this air recovers its former density, or when air of the ordinary state expands into double its volume. Hence the copious heat extricated by the sudden compression of air. If it were condensed thirty times, the heat discharged would amount to $25 \left(\frac{30}{30} - \frac{1}{30}\right)$, or 749°, which is more than sufficient for the inflammation of fungous or soft substances. On this principle, are constructed the pneumatic matches lately invented by Mollet of Lyons, which produce their effect by the momentary action of a small syringe.

But, to discover the relative capacity or attraction which air of a given density has for heat, it would be necessary to know the extent of the natural scale, or the position of the absolute zero. The conclusions, however, from different data, are not very constant; yet several experiments appear to fix nearly the point from which the infusion of heat commences at 750 centesimal degrees below congelation. On this supposition, therefore, air which is rarefied thirty times has its capacity doubled, the heat contained in it being dilated only fifteen times. For the same reason, air sixty times rarer than ordinary acquires a triple attraction for heat, which, in this union, becomes attenuated only twenty times. But these inferences are merely speculative, and the law of the gradation of temperature in the atmosphere is quite independent of the existence of an absolute term of heat.

The last formula now investigated has been already laid before the public, without any explication, however, or indeed indication, of the process by which it was discovered. The experiments on which it rests were begun many years since, and have been repeated with every precaution. But the mean results only are retained; and, for the sake of simplicity, a few slight modifications have been introduced, to adapt the apparatus to more convenient proportions. Though it was impossible to blow a receiver that should have exactly half the dimensions of another, nothing seemed easier, from the general mode of investigation, than to apply the minute corrections which any small deviations of size or form required. The mixture of obscure and intricate computations has been thus avoided.

The gradation of the effects disclosed by this experimental research, is more easily and clearly traced in geometrical diagrams. Having divided the abscissa AF into five equal portions, erect the several perpendiculars EG, DH, CI, BK, and AL, equal respectively to 9, 16, 21, 24, and 25 parts on any scale, and connect the points F, G, H, I, K, and L, by a curve line. It is readily perceived, that the curve now traced must be a parabola, formed on the axis LA. Wherefore, if AF represent the height of the barometric gage of the air-pump, and AD its altitude after a partial exhaustion, the parallel DH will express the rise of the included thermometer on the re-admission of the air which had been extracted. The axis AL itself denotes the extreme effect, or what would take place if the rarefaction were pushed to the utmost. While the mercurial column, therefore, descends by equal intervals to E, D, C, B, and approximates to A, the elevation of the thermometer through the spaces EG, DH, CI, BK, and nearly AL, advances at first uniformly, and afterwards continually more slowly, till it becomes stationary.

But the parallels to the axis of a parabola, do not express the whole of the heat disengaged by the attenuated air during the resumption of its density. The line DH, for instance, marks only the rise of temperature communicated to the entire mass AF, by the heat evolved from the portion AD; and to represent the true measure of this heat, it must, therefore, be increased in the ratio of AD to AF. Hence, from the point A, and through the extremities of the parallels EG, DH, CI, and BK, draw the oblique lines AG, AH, AI, and AK, to meet the extended perpendicular FO; the intercepted segments or parabolic tangents FM, FN, PO, and FP, (if this last were completed,) will exhibit the real portions of heat liberated from any of the corresponding densities AE, AD, AC, AB.

Let the part AL of the axis be taken equal to the farther parameter, and the ordinate AF must likewise be equal to it: Draw the vertical tangent LQ meeting the parallel DH in Q, join the oblique line AD, and produce it to meet the perpendicular in R. From the property of the curve, QH : AD :: AD : AF; but from the mutual relation of the diverging lines AN, AR, and the parallels DQ and FR, AD : AF :: AH : AN :: QH : NR; whence QH : NR :: QH : AD, and, therefore, NR is equal to AD. Consequently FN, which expresses the whole evolution of heat corresponding to the density AD, is equal to the difference between AD and FR. But since AD : AF :: DQ or AF : FR, the line FR is the reciprocal of AD, the parameter AF being considered as unit. The measure of heat evolved, or the parabolic tangent FN is, therefore, as before expressed, by the difference of the density of the air and its reciprocal.

The same result may be represented geometrically in another way. Let LIG be a rectangular hyperbola referred to its asymptotes AE and AF, the axis being AO: If the perpendicular IC, or the ab- sciss AC express the ordinary density of the air, and the ordinate DH denote any other density, the in- tercepted segment HN, or the difference between DH and its reciprocal AD or DN, will exhibit the additional share of heat required for its constitution. On the contrary, if the air acquires the higher den- sity BK, the quantity of heat which it must evolve in its transition will be represented by KP. In the figure here annexed, the air is presumed to have its density reduced to the half in one case, and doubled in the other, the quantities of heat, HN and KP, which are evolved and absorbed, being then equal and opposite.

Since the absolute quantity of heat contained in every part of any vertical column of the atmosphere has been shown to remain unchanged, these dia- grams must likewise represent the diminution of tem- perature in the higher strata, corresponding to the decreased density of the air at different elevations. The same formula will determine the measure and gradation of this effect. Reckoning the density of the air at the surface of the earth unit, the difference between the density at any given altitude and its reciprocal, being multiplied by 25, will express the mean diminution of temperature in centesimal de- grees; or if 45 be employed as the multiplier, the product will exhibit the same result in degrees of Fahrenheit's scale.

This very simple deduction from theory, is amply confirmed by numerous and extensive observations. But a few leading facts will perhaps be deemed suf- ficient for exemplification.

According to Lasius, the same barometer, which, at Goslar, an ancient town seated in the bosom of the Hartz Forest, stands at 29,500 inches, would fall to 26,444 on the top of the Brocken, in that Mining District. This gives .896 for the density of the air on the summit, the reciprocal of which is 1.116; but 1.116 - .896 = .22, and .22 x 25° = 5°.5, the calculated difference of temperature. The actual difference is very nearly the same, being only 5°.2; as we had once an opportunity ourselves of ob- serving, having found the temperature of a copious spring at Goslar to be 8 centesimal degrees, while that of the noted Hecken-Brunnen, or Witch-Well, on the summit of the Brocken, was only 2°.8.

Saussure, whose accuracy always inspires confi- dence, found that, while at his villa of Conche, near Geneva, the barometer stood at 28,500, an- other similar instrument fell to 25,165, on the top of the mountain of Nant Bourant. The dimi- nished density of the air at this elevation was, therefore, .890; the difference between which and its reciprocal 1.123 being multiplied by 25°, gives 5°.82. But a thermometer, buried a whole night at two feet deep, in that lofty station, marked only 12°.75; while it indicated 6.25 more, or 19°, a few days afterwards, when sunk to the same depth at Conche. The discrepancy here is thus less half a degree.

On the top of a higher mountain, the Chapieau, To the same observer found the ground, at a depth of pressure of two feet, to be colder by 6°.44 than at Conche. But the corresponding density of the air and its recipro- cal were 872 and 1.147; consequently, 25° x 275 = 6°.87.

While the barometer at Conche stood at 28,500 inches, the mercurial column was only 19,836 inches on the summit of Mont Cervin, a still loftier moun- tain. The density of the air at this elevation was therefore .696; which being taken from its recipro- cal 1.437, leaves 741 to be multiplied by 25°, indi- cating 18°.52 as the diminution of temperature. The actual medium difference ascertained from cor- responding thermometrical observations, made at depths in the ground, from one to three feet, on the top of Mont Cervin and at Conche, was 18°.25, al- most exactly the same.

Such is the nice agreement on the whole, between theory and observation, with regard to the decrease of the mean temperature in the higher regions of the atmosphere. This gradation of cold varies, however, to a certain extent with the seasons. Since the heat derived from the sun is chiefly accumulated at the surface of the earth, the changes of temperature which take place through the year in the elevated strata of our atmosphere, must evidently be less than what are experienced below. The lofty tracts of air, remote from the primary scene of action, preserve nearly an equable temperature, and scarcely feel the extreme heat of summer or winter's frost. In as- cending the atmosphere, the decrease of warmth is hence more rapid in the fine season, and more slow in the darkened period of the year. In many places, it will not be far from the truth, perhaps, to assume 30° for the multiplier during the summer months, and only 20° during those of winter.

Thus, General Roy, a diligent and experienced observer, found, in the month of August, the air on the top of Snowdon was, in the course of a whole day, at an average 7.2 centesimal degrees colder than on Carnarvon Quay. But the difference be- tween the density at that elevation, and its recipro- cal, or between .878 and 1.139 being only .261, would require nearly 28 for the multiplier.

In the early part of September, the same observer noticed the centesimal thermometer to stand 10 de- grees lower on the top of Ben Lawers than at Weem, the relative density of the air at that height being .868. The difference from its reciprocal is .284, which would hence require to be multiplied by 35 to give the actual diminution of temperature.

Again, Saussure found, on his visit to Mont Blanc, the air on its summit to be 31 centesimal degrees colder than at Geneva. The relative density was .592, which being taken from its reciprocal 1.689, leaves 1.097; consequently, the multiplier required is 28.

This ingenious philosopher passed several days encamped on the Col du Geant, where he found, from the mean of eighty-five observations, the temperature of the air to be only $4^\circ.54$, or $20^\circ.3$ colder than at Geneva. But the relative density of that elevated stratum and its reciprocal were $.704$ and $.420$; the difference of which, or $.716$, would require to be multiplied by 28, to indicate the diminished temperature.

The observations made on the decreased temperature of the higher regions of the atmosphere by the ascension of balloons, appear generally to indicate rather a slow rate of diminution. But it should be recollected that those daring aerial flights have seldom been performed except in the fine season of the year. Besides, the car, the balloon, and its cordage, will not immediately acquire the temperature of the elevated strata, but continue for a considerable time to diffuse a sensible portion of heat. A memorable example, however, is entirely conformable to the general principle. Charles, the first who ascended the atmosphere by means of a balloon filled with hydrogen gas, found, on the 1st of December 1783, the thermometer depressed 11 centesimal degrees at the greatest elevation, the column of the barometer having sunk from 29.24 to 20.05 inches. This would require a multiplier less than 20.

In ascending through equal heights, the density of the atmosphere, as derived from the incumbent pressure, diminishes in a continued proportion. This density is hence represented by the ordinates of a logarithmic curve, of which the absciss denotes the altitude above the surface. The cold which prevails in the upper strata would no doubt modify the dilatation of the air; but, since it follows nearly the same progression, it cannot materially affect the general results. In the figure annexed, the vertical spaces expressing the elevations of one, two, three, and four English miles; the horizontal lines 1D, 2F, 3H, 4K, represent the corresponding mean temperature in the temperate latitudes. But, from the nature of the logarithmic curve, if it were supposed to be continued in like manner below the surface, the horizontal lines at the same equal distances would be the reciprocals of the former. Let this extension of the curve be, therefore, folded back and placed over its first portion, rising from oA, and the difference between the horizontal lines, or the distance between the two branches of the curve, as, from the point A, they constantly spread from each other, will exhibit the diminution of temperature corresponding to the elevation. These branches of the curve at first diverge at the same angle; but the wider branch afterwards spreads with a larger sweep, and their mutual distance slowly increases.

This gradual increasing progression, which marks the diminution of temperature in ascending the atmosphere, is still more apparent from another property of the logarithmic curve. The difference between any two ordinates is constantly proportional to the intercepted area. Consequently, the successive diminution of temperature corresponding to the elevations of one, two, three, or four miles, are expressed by the areas ABDC, CDK, EFHG, and GHKI. But, since the component spaces 0C, 1E, 2G, and 3I, augment evidently faster than 0D, 1F, 2H, and 3K, diminish, the decrements of heat encountered in ascending the atmosphere must, on the whole, increase. It is farther evident, that, if those spaces were reduced to extremely narrow belts, they might be considered as proportional merely to their several lengths; and hence the momentary decrements, or the rate of the diminution of temperature at the heights of one, two, three, and four miles are expressed by the transverse lines CD, EF, GH, and IK. If a calculation be instituted for the temperate climates, while the mean temperature at the level of the sea decreases one centesimal degree during an ascent of 540 feet above the surface, it suffers a similar diminution in 529 feet at the altitude of a mile; but at two, three, four, and five miles of elevation, the same difference will obtain, at the contracting intervals of 498, 454, 401, and 346 feet. Should Fahrenheit's scale be preferred, those numbers multiplied by five, and divided by nine, will give respectively 300, 295, 277, 252, 223, and 192, for the ascents due to a decrement of one degree at the surface, and at the heights of one, two, three, four, and five miles.

Hence the altitude of any place above the surface of the ocean may be nearly ascertained from an observation of its mean temperature. In the milder climates, it will be sufficiently accurate, in moderate elevations, to reckon an ascent of 540 feet for each centesimal degree, or 100 yards for each degree on Fahrenheit's scale, of diminished temperature. Thus, the Black Spring, a copious perennial source which bursts forth on the ridge of the Pentland Hills, in the vicinity of Edinburgh, is found to indicate only 7°.2 centesimal degrees, or 1°.6 less than the medium due to that parallel. But 1°.6 multiplied by 540 gives 868 feet; which differs by a few feet only from the altitude, as determined by actual levelling. Again, we had ascertained the temperature of a plentiful and deep-seated spring in the meadow below Schweitz, near the margin of the branching lake of the Forest Cantons, to be only 10 centesimal degrees, or $3^\circ$ lower than the standard temperature of that latitude. This gives $\frac{3}{4} \times 540$, or 1890 feet, for the elevation of the central valley of Switzerland above the level of the sea.

As a final example, we may cite an observation made in Upper India by Dr Francis Buchanan, who found a spring at Chitlong, in the Lesser Valley of Nepal, to indicate the temperature of 14.7 centesimal degrees; which is $8^\circ$.1 below that of the standard of its parallel, or $27^\circ$, $38^\circ$. Therefore, $8.1 \times 540$, or 4374 feet, is the elevation of that valley.

When the altitude above the sea is very considerable, however, a multiplier somewhat decreasing from 540 must be taken. But it is easy to show, that the same result very nearly will be obtained, by applying a small correction. If the product of 540 into the diminution of temperature, be again multiplied by the square of this difference in centesimal degrees, and then divided by the constant number 15000, the quotient will express the quantity to be subtracted. Thus, in the last example, the square of 8.1 or 65.61 multiplied into 4374 makes 286978, and this divided again by 15000 gives 18, to be deducted from 4374, leaving 4356 for the corrected altitude.

This correction, therefore, amounts only to $3\frac{1}{2}$ feet at the elevation of one mile; but for two, three, four, and five miles, it would rise to 266, 904, 2128, and 3350 feet. Though it augments thus rapidly, it may in ordinary cases be totally disregarded, and the allowance of one degree by Fahrenheit's scale for every hundred yards of ascent, is a rule of most easy recollection.

That the decrements of heat, corresponding to equal ascents in the atmosphere, are not uniform, however, but augment gradually with an accelerating progression, is confirmed by the appeal to actual observation. Thus, in proceeding from Geneva to the Vale of Chamouni, through an elevation of 2094 feet, Saussure found the temperature of the air to decrease only $3\frac{1}{2}$ centesimal degrees, or at the rate of one degree in the rise of 644 feet. Between Chamouni and the Col du Geant, an interval of 7940 feet, the diminution of temperature was $17^\circ$, being a degree for each 465 feet of ascent. Again, the summit of Mont Blanc, though only 4400 feet higher than the Col du Geant, was $10^\circ$.8 colder; which gives a degree for every rise of 407 feet. The acceleration of cold is here very perceptible; but the gradation from Geneva to Chamouni was unusually slow, owing to the position of this sequestered spot, where the action of the sun-beams, in summer, being sheltered from the influence of dispersing winds, accumulates above the standard. Near the level of the sea, the ascent, corresponding to the decrement of a centesimal degree, very seldom exceeds 600 feet.

Since, in ascending from the surface, the temperature constantly diminishes, there must, in every latitude, exist a certain limit of elevation at which the air will attain the term of congelation. The mountains, likewise, which rear their heads above that boundary, are covered with eternal snow. In the higher regions of the atmosphere, especially within the tropics, the temperature varies but little throughout the whole year. Hence, in those brilliant climates, the line of perpetual congelation is strongly and distinctly marked. But, in countries remote from the equator, the boundary of frost rises after the heat of summer, as the influence of winter prevails,—thus varying its position over a belt of some considerable breadth.

The height of the limit of perpetual congelation for any latitude, is easily determined from the principles already established. Let $t$ denote the mean temperature in centesimal degrees at the surface of the ocean, and $x$ the density of the upper atmosphere at the line, where the reign of frost begins. It is evident from the formula, that

$$\left(\frac{1}{x} - x\right)^2 = t,$$

whence $x^2 + 0.04tx = 1$, and this quadratic equation being solved, gives $x = \sqrt{1 + 0.0004t^2} - 0.02t$.

From the density of the air thus found, the corresponding altitude is discovered by the application of logarithms, as in the barometrical measurements. Hence the following table is computed:

| Latitude | Height of Curve of Congelation, English Feet | Height of Curve of Congelation, English Feet | |----------|---------------------------------------------|---------------------------------------------| | 0 | 15207 | 32° | | 1 | 15203 | 33 | | 2 | 15189 | 34 | | 3 | 15167 | 35 | | 4 | 15135 | 36 | | 5 | 15095 | 37 | | 6 | 15047 | 38 | | 7 | 14989 | 39 | | 8 | 14923 | | | 9 | 14848 | | | 10 | 14764 | | | 11 | 14672 | | | 12 | 14571 | | | 13 | 14463 | | | 14 | 14345 | | | 15 | 14220 | | | 16 | 14087 | | | 17 | 13947 | | | 18 | 13798 | | | 19 | 13642 | | | 20 | 13478 | | | 21 | 13308 | | | 22 | 13131 | | | 23 | 12916 | | | 24 | 12755 | | | 25 | 12557 | | | 26 | 12433 | | | 27 | 12145 | | | 28 | 11930 | | | 29 | 11710 | | | 30 | 11484 | | | 31 | 11253 | | This table, though calculated from theoretical data, will be found to coincide with actual observation. It suggests a variety of important results; and the position of the snowy boundary may direct the intelligent traveller to estimate the elevation of any country. Thus, Ben Nevis, the highest mountain in Scotland, is generally seen covered with snow through the whole year, except during two or three weeks in the month of July. Its summit, therefore, does not reach the limit of congelation, which, at the latitude of 57°, has an altitude of 4534 feet. Accordingly, the height of that mountain is only 4380 feet. Again, we learn from the relations of travellers, that, though perpetual snow covers the stupendous ridge of the Himalaya mountains in Upper India, it descends but a short way along their sides, and leaves, for the ghauts or passages below, a grassy plain. But the boundary of congelation traverses the parallel of 30° at the altitude of 11,484 feet, and consequently that towering range may rise probably 4000 or 5000 feet higher, and thus surpass the elevation of Mont Blanc. The pretended altitudes of 23,000 or even 27,000 feet, so recently assigned to those mountains, are hence utterly incredible.

The gradation of altitude which marks the snowy boundary in different latitudes, is most clearly perceived from the inspection of a diagram. Thus, if every intermediate point B be determined, by making any parallel 10 AB equal to the intercepted arc A 29. If the absciss then represent the meridian extending from the equator to the pole, the several ordinates will express the corresponding mean temperatures at the level of the sea. The reason of this construction is easily perceived; for the arc O A of the generating circle being equal to the complement of the corresponding latitude, its chord is equal to the cosine of this latitude, which belongs to a circle having twice the diameter of the former; but the ordinate from B, or the perpendicular segment O 10, is proportional to the square of the chord O A, and consequently to the square of the cosine of the latitude.

The curve now constructed is what has been called the Companion of the Cycloid. In fact, it differs from the cycloid only by the defect of the generat- ing circle. If each parallel AB were extended as far beyond B as 10 A, the cycloid would be traced. This deficient cycloid has obviously the same aspect as the curve of perpetual congelation. It is only less flattened towards the equator, where the correction of altitude chiefly operates. A close inspection, however, is requisite to distinguish their difference.

The companion of the cycloid, or curve of temperatures, might also be formed, by unrolling half the convex surface of a cylindrical wedge or angula. The curve, already delineated, was only the expansion of the annexed figure.

If the semicircumference of the base of the cylinder were divided into 90 equal parts, to denote the successive latitudes from the equator to the pole, the perpendicular lines terminating in the oblique section, would express the corresponding mean temperatures. These lines, again, might be easily measured by parallels of temperature or arcs of circles, dividing the altitude of the wedge into 29 equal parts, and running parallel to the plane of its base. If the whole wedge or ungula were taken, the combination of vertical lines and horizontal arcs, would exhibit all the gradations of mean temperature, in its progress and subsequent decline from pole to pole. It is easy to perceive, that, on this plan, an elegant instrument could be constructed, equally calculated for illustration and practical use.

The curve of perpetual congelation must evidently rise higher during the tide of summer, and again descend in the winter months, thus oscillating between certain limits of elevation. The intervening belt is narrow under the equator; but it enlarges to a very considerable extent in the higher latitudes. On the breadth of this zone, where frost holds a doubtful reign, depends the formation of glaciers, along the flanks of the snowy mountains. The fields of snow, which are alternately melted and congealed, become at last changed by this process into solid ice, often grouped and fashioned by such irregular action into the most fantastic shapes. In its native seat, this icy belt acquires continual additions to its height, till the accumulating pressure at last tears the mass from its base, and precipitates its dissevered fragments to a lower level. In its new position, below the inferior boundary of congelation, the enormous pile suffers, on the whole, a very gradual thaw, which is sometimes protracted for several centuries. Meanwhile, in the higher magazine, another icy belt is again slowly collecting, which will in due time repeat the succession, and maintain the eternal circle of production and decay.

Within the tropics, the zone of undecided frost is so very narrow, that scarcely any trace of a glacier has been ever observed. But as that zone enlarges in the higher latitudes, the appearance of vast glaciers constitutes a very striking feature in the aspect of the lofty mountains. They occur frequently along the sides of the Pyrenees; but they are still more conspicuous in the recesses of the central chain of the Swiss Alps. Glaciers are likewise seen as far north as the verge of the Arctic Circle. Along the western shore of Norway, and the coast of Lapland, stretching onwards to the promontory of the North Cape, huge masses of columnar ice descend from the cliffs, or against the precipitous sides of the mountains, almost to the surface of the ocean.

Through the whole train of investigation now heatedly pursued, the warmth which vivifies our globe has been viewed as flowing from the fountain of the Sun. The easiest mode of conceiving the subject is to consider the Heat which permeates all bodies, and unites with them in various proportions, as merely the subtle fluid of Light, in a state of combination. When forcibly discharged or suddenly elicited from any substance, it again resumes its radiant splendour. Such changes are exhibited in the phenomena of Electricity, and in many of the operations of Chemistry. But the production of Light is not less striking in the ordinary business of life. The glowing spark struck from flint, and the consuming fire, which even the rudest tribes had learned to excite by the rapid friction of two pieces of dry wood, were by the ancient philosophers regarded as only detached portions of the divine and celestial flame which illumines the empyreal vault. The same notion was embraced by the poets, and gives sublimity to their finest odes. Heavenly Light, Invisible Light, and the Light of Life, are lofty and refined expressions, which gleam through the mystic hymn of Orpheus.

These poetical images which have descended to our own times, were hence founded on a close observation of nature. Modern philosophy need not disdain to adopt them, and has only to expand and reduce to precision the original conceptions. If any body be exposed to the sun's incident rays, it will experience a rise of temperature exactly proportioned to the quantity of light intercepted or absorbed. When those rays are either concentrated or attenuated, the effect produced by their detention is proportionally augmented or diminished. The calorific action is occasioned solely by that portion of the light which remains united to the opposing substance. The rays which are either transmitted or reflected, leave no trace of their energy. Neither a very bright reflecting surface, nor a fine pellucid medium, is sensibly heated on being exposed even to a meridian sun. But since reflection and transmission cannot be perfect, a certain calorific effect, however small, and varied by circumstances, is always the result. A polished surface of silver may absorb from the tenth to the fifth part of the perpendicular rays; and we have seen that the thin body of atmosphere itself will detain one-fourth part of the vertical light shot down through it, and one half of the beams that slant at an inclination of 25°. The absorption of light in its passage through water is proportionally greater; the perpendicular rays lose half their force by a descent of 17 feet in that medium; become reduced to one-fourth by traversing a path of 34 feet, which corresponds to the mass of an atmosphere. It hence follows, that only the hundred thousandth part of the vertical rays can penetrate below 47 fathoms. But this faint remnant is scarcely equal to the glimmer of the closing twilight. The depths of the ocean are never visited, therefore, by the cheering influence of the great luminary of day.

The rise of temperature produced by the same measure of the absorption of light, is in different substances inversely as their capacity or attraction for heat. Thus, if two very thin glass balls of the same diameter, and coated with China ink, be filled, the one with water and the other with mercury, and exposed to the sun, the latter will mark an accession of five degrees of heat, while the former will indicate only two. Or, if two equal and similar pieces of glass and lead were both of them blackened and presented to the incident solar rays, the lead will acquire a higher temperature than the glass, in the ratio of 12 to 7.

This theory agrees, therefore, in all its bearings, exactly with observation. But facts have been alleged, of a contrary tendency; and some ingenious, yet incorrect experiments, performed by a celebrated astronomer, appear to have, for several years, deceived the public into a belief, that, besides the ordinary mixture of coloured rays emanating from the sun, there is emitted also a cluster of invisible and less refrangible rays, which excite or constitute heat.

As if such an hypothesis were not already sufficiently complex, it was afterwards assumed, that there exists likewise another series of dark rays, more refrangible than usual, whose office it is merely to abstract oxygen from the substances on which they fall. But a closer examination of the circumstances have proved, that, in forming these opinions, philosophers have proceeded to generalize too fast. If, while the sky is perfectly clear, which seldom happens indeed in this climate, the solar spectrum formed behind a prism be observed by a differential thermometer in a darkened room, the intensity of the heat will be found to augment most rapidly in passing from the one extremity to the other, from the limit of the violet to that of the red. When a prism of flint-glass was used, we found that the spectrum being divided into four equal spaces, the effects indicated by the thermometer, and corresponding to the range of the violet, the green, the yellow, and the red, were as the square numbers 1, 4, 8, and 16. If the spectrum were formed by another refracting medium, as the intermediate coloured spaces would alter their proportions, so likewise would the calorific action vary. But, in every case, the violet and the red rays which occupy the extremes, must differ very widely in their relative energies. Without the spectrum, however, and beyond the absolute limit of illumination, no sort of action whatever is betrayed. The mit of the distinct effects produced by the extreme coloured Spectrum spaces may possibly depend on the peculiar qualities of the several rays; but, perhaps, proceed from the character of the diluted or concentrated energy which they display. The violet, or blue, rays will probably hasten the process of darkening a solution of the nitrate of silver; yet have we found, that white light, attenuated to a certain degree, has likewise a power to accelerate this change. It is probable that the collected beams only retard the effect, by exciting heat, which may dispose the oxygen to adhere more strongly to its substratum. In like manner, the intense action of the red rays on the bulb of a thermometer may proceed more from their condensation than from some exclusive quality which they possess. What is the nature of that peculiar constitution which fits a ray of light to excite in the organ of

---

* It may be worth while to state here a very simple, yet decisive experiment, which we have repeated more than once. If a circle of black paper, ten inches in diameter, be pasted over the middle of a burning glass of the diameter of one foot, it will leave, around the margin of the lens, a sort of circular prism, which bends the coloured rays into a hollow double cone, whose intermediate apex occupies the focus. On directing the lens, thus partly shaded, to a bright sun, in a clear sky, a card held perpendicular to the beam, and drawn either forwards or backwards from the focus, will exhibit a narrow coloured ring, opening with intense brilliancy. Between the focus and the lens, the red rays will mark the outer edge of the vivid ring; but beyond that limit, they will cross over and tint the inside. In either case, it was easy to mark their extreme boundary. To examine the graduating calorific action of this condensed spectrum, a broad and flat piece of black sealing wax, having the gloss removed from its surface by a file, and a thin slip of white paper laid across it, was then held in the cone of light, two or three inches before the focus, and in the space of a few seconds a very narrow ring, shading inwards however, was distinctly impressed in the wax, the roughened surface being melted and left hollow and glossy, at the exact limit of the red on the outside, and smoothing slightly away on the inside. Beyond the apex of the double cone of light, a similar glazed narrow ring was imprinted, softening from the inside. In both cases, the circular impression on the wax corresponded exactly with the trace of the red rays,—an interval of the fiftieth part of an inch being easily distinguishable. vision any peculiar sensation of colour, it seems impossible to decide. Perhaps the whole distinction consists in the difference of the celerity with which it moves. The peculiar energy of any coloured pencil of light may depend chiefly, if not entirely, on its density. From the violet to the red, the successive tints of the spectrum rise with augmented force. The blue rays appear feeble, the green cause a milder impression, the yellow and the orange begin to glow with intensity, and the red dazzles the eye. The language of painters, being grounded on nice observation, marks appositely the gradation of strength. Blue is by them termed a cold colour, green a soft colour, yellow a rich colour, and red a warm colour.

For measuring the intensity, or at least the calorific action of light, no instrument is so finely adapted by its peculiar delicacy as the Photometer, which consists of a Differential Thermometer, inclosed in a thin pellucid case, and having one ball made of black and the other of clear glass. It will besides admit of some variety in its form and construction, and may be rendered on the whole very commodious and portable. Yet, owing to a combination of circumstances, this elegant instrument has only been partially and reluctantly admitted; and the philosophic world has still to discharge an act of justice, by receiving it into the favour and distinction which it so well deserves. Some indeed, affecting to display superior sagacity, have taken the trouble to remark that it was only a species of thermometer, and not strictly a photometer, since it measures heat and not light. But what does the thermometer itself, except indicate expansion? As heat is measured by the expansion it occasions, so light is determined by the intensity of the heat which, in every supposition, invariably accompanies it. What other mode, after all, could be imagined for detecting the presence of light? How can an unknown quantity be expounded, but in terms of one already known?

The photometer is adapted for a variety of important meteorological researches. If such instruments, in the hands of skilful observers, had been dispersed to the remote regions of the globe, we should ere now have obtained a body of precise facts, highly instructive in themselves, and calculated to illustrate the nature of different climates. Meanwhile, we shall endeavour to state the general consequences which may be drawn from even a scanty range of photometrical observations.

The direct and absolute action of the sun's rays on the photometer, at the elevation of 30°, may be reckoned in this climate at 120 millesimal degrees. The effect is produced by the incidence of a pencil of light, which has for its base a circle of the same diameter as the black ball, but modified and regulated in its amount by the subsequent dispersion of the accumulated heat from the whole surface of the sphere, which is four times greater than that of the generating circle. If a thin disc were, therefore, substituted instead of the ball, and presented to the perpendicular rays of the sun, the impression would be doubled or raised to 240°; or, if the emission of heat from the posterior surface of the disc were prevented, the calorific effect would amount by this accumulation to 480°, or 86 degrees on Fahrenheit's scale. Such is the rise of temperature which a dark surface of dry mould sloping at an angle of 30°, yet exactly facing the sun, might acquire under a diaphanous shell of glass, if scarcely any portion of the heat were supposed to be conducted downwards into the mass of the earth. But since the rays of light which traverse the atmosphere under an obliquity of 30° have, in comparison with perpendicular beams, their force diminished in the ratio of 750 to 563; the action of a vertical sun, through a thin capsule of glass, might heat up a dark horizontal surface 113° by Fahrenheit's scale. On removing the glass cover, this effect, in a calm still air, would be reduced about two-thirds or to 75°.

The colour of the ground or substratum has very little influence in modifying the calorific action of the solar beams. The different shades of brown or gray have almost the same absorbent quality as black itself; yellow and orange begin to cause a partial reflection; but a surface even of pure chalk will not reflect perhaps the fifth part of the incident light. Hence the arid sands of Africa are often heated by a vertical sun to near the point of boiling water; in so much as to scorch the feet of the wretched traveller, and to accumulate warmth sufficient for the slow roasting of an egg. Even within the Arctic Circle, the calorific action of a bright sun, in the height of summer, may exceed 49°. In those dreary regions, accordingly, amidst a dissolving world of ice, the pitch is yet sometimes softened or melted, in the seams of the sides or the decks of ships.

It is obvious that the accumulated effect of the incident rays, must increase in proportion as the conducting power of the medium is diminished. Hence at an elevation of three miles and a half, where the density of the atmosphere is reduced to one-half, the heat communicated would, on this account alone, augment from 75° to 83 degrees. But the effect would be farther increased, from the smaller absorption of heat in its passage to the surface. Under the equator, the whole accumulated action would, therefore, amount to 96 degrees. All travellers, accordingly, complain of the scorching rays which the sun darts from a dark azure sky on the summits of lofty mountains. Yet the contrast is more striking in the higher latitudes. Thus, in the middle parallel of 45°, the action of the sun at the summer solstice would excite a heat of 69° at the level of the sea, and of 90° at an elevation of three miles and an half; but, at the winter solstice, it would communicate only 17° below and 46° at the altitude assumed. Saussure was accordingly very much struck with the force and brilliancy of the sun-beams on the top of Mont Blanc.

It might easily be computed that, on the supposition of a perfect calm, the surface of the earth, under the equator, will, at the medium of a year, have its temperature raised 12°; and that, in the latitude of 45°, the mean annual impression would be only 5°. But, of the whole of the light received, the calorific action on a black mould, whether emitted from the sun or shed indirectly by the sky, may be deduced from the indication of the photometer. It is only required to diminish the power of the sun's rays in the ratio of the sine of their obliquity, and to reduce the action of the light reflected from the canopy of clouds to one-half; or what is due to the medium inclination of 30°, then to multiply the sum of these quantities by eight, and divide by three, or to take two-thirds of the quadrupled effect. Thus, suppose, while the sun's altitude is 40°, that the photometer marks 155°, which it very seldom ever reaches in this climate, and that it indicates only 20°, if merely screened from the direct action of the sun. Now, 155° multiplied by the sine of 40°, makes 87°-8, which is augmented to 97°-8 by the addition of the half of 20°, and this number again being increased in the ratio of 3 to 8, gives finally 261 millesimal degrees, or 47° on Fahrenheit's scale.

When the sun is obscured in clouds, the reflected light, from a dappled sky, will sometimes in summer affect the photometer to the extent of 40°. This corresponds to a heat of 16 degrees of Fahrenheit communicated to the ground. During the fine season, the photometer seldom in cloudy weather indicates less than 15°, which is equivalent to an impression of 6 degrees on the embrowned surface of the earth. While the sun is enveloped in clouds, if the rest of the sky assumes a fine azure hue, the photometer will only mark 10°. But in the gloomy days of winter, the minute portion of light which pierces through the congregated mass of clouds will scarcely affect the photometer 5°, or excite a heat of 2° by Fahrenheit on the ground.

These augmentations of temperature are communicated to the ground unimpaired, only in the case, however, of a perfect calm. The agitation of the atmosphere will scatter the heat before it has accumulated. When the wind creeps along the surface of the earth at the rate of eight miles in the hour, it diminishes the calorific action of the light from the sun and from the sky one-half; but if it sweeps with a velocity of 16, 24, or 32 miles in the hour, it will reduce the whole effect successively to the third, the fourth, or the fifth of its standard. The impression made on the ground seldom, therefore, exceeds the third part of the computed measure, and often will not amount to one-fifth.

The simplest and most accurate method of examining the temperature acquired during the day on the surface of the earth, is to employ a differential thermometer of the pendant kind, having about one or two feet in length, and its lower ball surmounted by a small cylindrical cavity supporting the coloured liquor. This instrument being suspended or held in a vertical position, the lower ball resting on the ground, will evidently mark, by its moveable column, the difference between temperature of the surface and that of the ambient air. In this way, we have found, during the summer months in this climate, that the ground was, by Fahrenheit's scale, generally two or three degrees warmer than the air near it in cloudy weather, and perhaps ten or fifteen degrees warmer when the sun shone powerfully upon it. But, under similar circumstances, the effect varies very considerably, according to the nature of the surface. While fresh ploughed land, for instance, indicates an increased temperature of perhaps 8°, a grass plot close beside it will scarcely show a difference of 3°. Nor is this distinction owing to any greater absorption of light by the black mould; the reflexion from the surface, in both cases, being extremely small. A thin layer of hay, whether spread on the naked soil or on the green turf, will betray the same diminished effect. The fibres of the grass exposing a multiplied surface to the contact of the air, the greater portion of the heat is hence dissipated before accumulation. A corresponding effect has been remarked with respect to the impressions of cold. Thus, in the neighbourhood of quality of Edinburgh, after a long tract of rigorous weather, the frost was found to have penetrated 13 inches into the ground in a ploughed field, but only 8 inches in one piece of pasture ground, and 4 inches in another. But, in some of the streets of that city, the frost had descended even below two feet, so as to begin to affect the water pipes. The greater density and solidity of the pavement had no doubt conducted the frigorific impressions more copiously downwards, while the loose and spongy blades of grass had mostly scattered and wasted those impressions in the open field. This consideration, it is obvious, might lead to very important practical results.

The unequal action of light at the surface of the earth, whether produced by the various obliquity of the sun's rays, the different inclination of the horizon, or the alternating succession of day and night, is attempted, we have seen, by the actual flow of the heated portions of the atmosphere. Between the poles and the equator, a perpetual circulation of air between the poles and the equator is maintained, which confines the accumulating effects of heat within narrow limits. The prevalence, the Equator on the whole, of northerly winds in this hemisphere during summer, and of southerly winds in winter, tends likewise to mitigate the extreme impressions of hot and cold. But a current of warm air excited at first by the presence of the sun, continues to rise from the ground, and occasions the descent, therefore, of an opposite current of cold air, which, as the equilibrium of temperature is not soon restored, may be protracted through a great part of the night. The combined influence of these currents is hence continually exerted, in cooling down the surface of the earth; but their activity being the greatest while the solar beams fall most copiously, the accumulation of heat is checked in little more than an hour after mid-day, while its farther dissipation is prolonged through the whole of the night, sun-rise being generally the moment when the ground is coldest.

Such a concatenated system of aerial currents might hence appear sufficient to explain the gradation and general balance of temperature which prevails on the surface of our globe. An horizontal stream of air must evidently cause the flow of an opposite one, since the action must be the same on every part of the same parallel of latitude. The difference of the temperature of the surface from that of the ambient air will maintain the constant play of an ascending and a descending current. In clear and calm weather, this interchange between the higher and lower strata of the atmosphere will be the most vigorous, owing then to the concentrated impression of the sun-beams. The perpetual commerce maintained in our atmosphere by the medium of these combined horizontal and vertical currents, forms no doubt an essential part of the system which tempers the constitution of this globe. But it is not the only mode by which... nature seeks to preserve the harmony of her productions; and recent discovery has detected the existence of another auxiliary principle, extremely active, of most rapid and extensive influence, and continually at work, though subject to various modifications. To understand rightly, however, the operation of this principle, it will be necessary to recall the chief facts which have lately been disclosed relative to the Propagation of Heat.

It is well known, that, though partial causes may disturb the equilibrium of temperature among bodies, there is a constant tendency to restore it again. Yet heat still remains in the state of combination, without ever assuming a distinct form. Its balance is, therefore, maintained by a very different process from that which establishes the equilibrium between the several communicating parts of a liquid. The substratum of heat is not passive, nor do the calorific particles themselves merely flow from their redundancy towards another situation where they happen to be deficient. But since the presence of heat is invariably accompanied by corporeal distention, that portion of the substance which loses it must successively contract, while the portion which gains it will in the same degree expand. The actual transfer of heat through any mass will hence give occasion to a connected series of minute internal contractions and expansions. To consider the subject more fully, we shall suppose the conducting substance to be, 1. A solid; 2. A liquid; and, 3. A gaseous fluid.

1. Through Solids:

When the surplus heat is conducted through a solid substance, a sort of alternating vermicular motion is excited along the whole train of communication. If heat were left to the energy of its own repulsion, it would, like light, dart with a speed almost instantaneous. But the time consumed by these interior oscillatory movements retards immensely the rate of transmission. The quickness of the oscillations themselves depends on the elasticity of the conducting substance; but their energy and extent are proportioned to the extreme difference of temperature, and the shortness of the tract, modified essentially by the peculiar nature of the conducting substance. In equal circumstances, glass transmits heat faster than wood, and metal faster than glass. But, even in the same class of conductors, the effects are very different; thus, box delivers the impressions of heat more quickly than cork, and silver conveys them with greater rapidity than platinum.

2. Through Liquids:

The ordinary transmission of heat through a solid, is now greatly augmented from the diffusion occasioned by the mobility of the affected portions of the medium. Below the freezing-point, ice will conduct heat through its substance; but, after it has melted into water, a new and powerful agency is brought into play. The liquid particles, as they become successively warmer, acquire a corresponding expansion, and, therefore, rise upwards and spread through the mass, carrying with them and dispersing the heat which they have received. This diffusive buoyancy will depend evidently on the dilateable quality of the liquid. It is greater in alcohol than in water, and in water than in mercury; it is even more active in hot than in cold water. Near the point of congealation, indeed, the joint conducting power of water is scarcely superior to that of mere ice. The actual flow of a liquid, by whatever cause it is produced, must evidently accelerate the dissipation of heat.

3. When the medium of transmission is a gaseous substance, the heat is partly still conducted through the substance of the communicating mass, as if it were solid, and partly transferred by the streaming of the corpuscles, which come to be successively affected. But a new principle seems here to combine its influence, and the rate of dispersion in aeriform media is found to depend chiefly on the nature of the heated surface. From a metallic surface, the heat is feebly emitted; but, from a surface of glass, or still better, from one of paper, it is discharged with profusion. If two equal hollow balls of thin bright silver, one of them entirely uncovered, and the other closely enveloped in a coat of cambric, be filled with water slightly warmed, and then suspended in a close room, the former will only lose 11 parts of heat in the same time that the latter will dissipate 20 parts. Of this expenditure, 10 parts from each of the balls is communicated in the ordinary way, by the slow recession of the proximate particles of air, as they come to be successively heated. The rest of the heat, consisting of 1 part from the naked metallic surface, and of 10 from the cased surface, is propagated through the same medium, but with a certain diffusive rapidity, which in a moment shoots its influence to a distance after a mode altogether peculiar to the gaseous fluids.

But those effects are modified by the different proximity of the air to the metallic surface. If the silver ball be covered with the thinnest film of gold-beater's skin, which exceeds not the 3000th part of an inch in thickness, the power of dispersion will be augmented from 1 to 7; if another pellicle be added, there will be a farther increase of this power, from 7 to 9; and so repeatedly growing, till after the application of five coats, when the repellent energy will reach its extreme limit or the measure of 10.

The approximation of the metallic substratum thus evidently diminishes the power of the external pellicle in darting heat. No absolute contact exists in nature; but air must approach to a boundary of pellicle, or cambric, much nearer than to a surface of metal, from which it is always divided by an interval of more than the 500th part of an inch. A vitreous surface has very nearly the same property as one of cambric or paper; from its closer proximity to the recipient medium, it imparts its heat more copiously and energetically than a surface of metal in the same condition.

By what process the several portions of heat thus delivered to the atmosphere, shoot through the fluid mass, it seems more difficult to conceive. They are not transported by the streaming of the heated air, for they suffer no derangement from the most violent agitation of their medium. The air must, therefore, without changing its place, disseminate the impressions it receives of heat, by a sort of undulatory commotion, or a series of alternating pulsations, like those by which it transmits the impulse of sound. The portion of air next the hot surface, suddenly acquiring heat from its vicinity, expands proportionally, and begins the chain of pulsations. In again con- tracting, this aerial shell surrenders its surplus heat to the one immediately before it, now in the act of expansion; and thus the tide of heat rolls onwards, and spreads itself on all sides.

But these pulsations are not propagated with equal intensity in all directions. They are most powerful in the perpendicular to the projecting surface, and diminish as they deviate from that axis in the ratio of the sine of the angle of obliquity.

Nor are the vibratory impressions strictly darted in radiating lines, but each successive pulse, as in the case of sound, presses to gain an equal diffusion. Different obstructions may hence cause the undulations of heat to deflect considerably from their course. Thus, if a cornucopia, formed of pasteboard, present its wide mouth to a fire, a strong heat will, in spite of the gradual inflection of the tube, be concentrated at its narrow end; in the same way, probably, as waves, flowing from an open bay into a narrow harbour, now contracted and bent aside, yet without being reflected, rise into furious billows.

But the same pulsatory system will enable the atmosphere to transmit likewise the impressions of cold. The shell of air adjacent to a frigid surface, becoming suddenly chilled, suffers a corresponding contraction, which must excite a concatenated train of pulsations. This contraction is followed by an immediate expansion, which withdraws a portion of heat from the next succeeding shell, itself now in the act of contracting; and the tide of apparent cold, or rather of deficient heat, shoots forwards with diffusive sweep.

That quality which enables a surface to propel the hot or cold pulses, likewise fits it under other circumstances to receive their impressions. If a vitreous or varnished surface emits heat most copiously, it will also, when opposed to the tide, arrest, with entire efficacy, the affluent wave; and if, on the other hand, a surface of metal sparingly parts with its own heat, it detains only a small share of each warm appulse, and reflects all the rest.

Hence the construction of the Pyroscope, a delicate and valuable instrument, adapted to measure the warm pulses of air, or the intensity of the heat that darts continually from a fire into a room, which has been vaguely and inaccurately termed radiant heat. It is in fact only a modification of the differential thermometer, one of the balls being completely gilt with a thick gold or silver leaf. The pyroscope being placed at some distance from the fire, the hot pulses are mostly thrown back from the bright metallic surface; but, on the naked glass ball, they produce their full impression. But the same instrument will serve equally to indicate the pulsations excited from a cold surface. Thus, in a warm apartment, the pyroscope placed before a mass of snow, a block of ice, or even a pitcher of water from the fountain, will quickly intimate the chilling impressions propagated through the ambient medium. Nor has the brightness of the fire or the glare of the snow any sensible influence to affect the result, for, of the small portion of light transmitted, what falls on the diaphanous ball passes almost without obstruction, and what strikes the gilt ball, especially if this be covered with silver leaf, is nearly all reflected.

But the pyroscope, in its simple form, is scarcely calculated for making nice observations, when exposed out of doors to the agitation of winds and the effulgence of light. A greater share of this light will generally be detained by the gilt surface than what is absorbed in its passage through the diaphanous ball. On the other hand, all the effects on the instrument will be diminished by the rapidity of the circulation of the air.

The application of the pyroscope incontestibly shows, that no pulsation, whether calorific or frigorific, ever takes place, except from a conterminous surface, which is either hotter or colder than the surrounding gaseous medium. If the general equilibrium of temperature be interrupted, such aerial pulses will arise, whether the boundary of excitation be solid or liquid. They are produced feebly from a surface of metal, though evidently stronger from mercury than from silver; but they are projected with most energy from a surface of glass, and still more powerfully from one of varnish, of paper, of ice, and of water.

But since those hot or cold pulses are darted from surfaces of such various surfaces, and since the softness of the external coat, and its tendency to fluidity, seem vastly to augment their power; may they not likewise be excited from a boundary of air itself? This sphere of extension of a great principle in the economy of nature has never yet been surmised; nor can it be readily brought to the test of direct experiment. A body of air, whether hotter or colder than the general medium, it is evident, could not remain for a moment in the same detached situation, but would continue to rise or to fall. In a confined place, however, a stratum of warm air may float incumbent over a mass of colder fluid. The difference of temperature between the conterminous surfaces, would no doubt be constantly diminishing from the slow intermixture and subsequent diffusion of the adjacent portions of the air. This tendency to an equilibrium might be counteracted, by causing either a constant stream of warm air to enter by the edges of the ceiling of the apartment, or one of cold air to flow from the side of the floor. Such would be the most favourable arrangement for performing the experiment. Both the ceiling and the floor would obviously soon acquire the same temperature as the current spreading over them, and could therefore exert no influence whatever in projecting the aerial pulses. If, under such circumstances, those pulses be hence found to exist, they must necessarily proceed from the action excited at the bounding surface which divides the warm from the cold stratum of air.

But an arrangement, less perfect indeed, yet sufficient for ascertaining the main fact, is entirely within our reach. In a close apartment, where a good fire is constantly kept up, the ceiling and the floor may be discovered by the pendant differential thermometer to have exactly the same temperature with its adjacent stratum. Yet the upper portions of the confined air of the room will be found several degrees warmer than the lower. Instead of being divided only into opposite ranges, the whole mass, from the floor to the ceiling, will, in consequence of the expansion and buoyancy of its heated particles, form a series of intermediate strata, not distinguished, however, by any very precise boundaries. But the intensity of action being proportional to the difference of temperature, the effect on the pyroscope must evidently be the same, whether it is produced by a single set of large pulses or by several sets of smaller ones. If, instead of one bounding surface, for example, above which the air is six degrees warmer than immediately below it, we suppose six such boundaries, each having an excess of temperature of only one degree; the pulses excited at the first of these intermediate surfaces, and successively augmented as they reach the second, third, and fourth, &c., surfaces, will at last acquire the same energy as if the aggregate difference of six degrees had been all exerted at once. Thus, the under surface of the stratum F darts pulses downwards, which, being augmented in succession at the under surfaces of the strata E, D, C, B, and A, may have finally the same intensity as if they had originated from the apposition of the extreme strata F and A. Accordingly, having planted a large screen immediately before the fire, if a delicate pyroscope be placed about the middle of the room, and a broad circular piece of metal suspended a few inches above it; on withdrawing this canopy after some time, the instrument will indicate a small impression of heat, seldom exceeding, however, one degree. But the effect may be rendered more sensible by a moderate concentration of the power excited.

Suppose a hemispherical shell of thin brass, or even planished tin, having a diameter about four times greater, adapted under the naked or sentient ball of the pyroscope, which might occupy, by its surface, the place of the diffuse focus, or the middle space between the centre and the bottom of the cup. Thus mounted, the instrument will now, in the same situation, mark a very sensible calorific impression, amounting, at least in ordinary cases, to 3 or 4 degrees. Hot pulses are, therefore, actually shot downwards from all the upper strata of the confined air of a room in which a fire is kept steadily burning.

The experiment can be likewise reversed. Let an inverted pyroscope, composed of a pendant differential thermometer, have its sentient ball fitted with a small hemispherical cup which is turned downwards. This instrument being set on the floor, will remain at zero; but if lifted only a few feet, it will indicate a visible impression of cold received from below, which will increase to 3 or 4 degrees when the pyroscope is suspended near the top of the room. Wherefore, the upper surfaces of the successive decumbent strata, being comparatively colder, send upwards a series of chilling pulsations. Each of the conterminous boundaries appears thus to perform a double operation, shooting downwards impressions of heat, and darting upwards equal impressions of cold. Such a mutual exchange of influence must evidently tend to accelerate that progress to an equilibrium which the gradual intermixture of the different strata, if left quite undisturbed, would in time produce. The air of a close apartment exposed to the action of a steady fire, is hence kept agitated through its whole mass by a series of opposite tremors, which continually disperse, in all directions, the irregularities of temperature.

If the action of the pulses excited in the air of a small room be made thus apparent, how much more striking should we expect to find the effect produced by the mingled tide of commotion collected in free space from the vast body of the atmosphere itself? Taking even the lowest range of strata, to the height perhaps of two miles, including scarcely one third part of the whole aerial mass, the difference of temperature between its extreme boundary will amount to 20 centesimal degrees, or 36 on Fahrenheit's scale. The order of the series, however, is exactly the reverse of what takes place in a close room, the air of the superior regions being invariably colder than at the surface of the earth. Accordingly, the simple pyroscope, exposed in calm weather to a clear and open sky, will, at all times, if not disturbed by the influence of a strong light, indicate large impressions of cold, amounting to 5 or perhaps even 10 degrees. In most cases, it may be sufficient to screen this instrument from the direct action of the sun's rays. But the action of light will be almost neutralized, by opposing a diaphanous ball to one gilt with silver, or contrasting a ball of the different shades of green or blue, to another coated with pure gold leaf. But to procure consistent results, it is still more necessary to guard against the deranging influence of winds.

All these requisites are attained by adapting the pyroscope to the cavity of a polished metallic cup, of rather an oblong spheroidal shape, the axis, having a vertical position, being occupied by the sentient ball, while the section of a horizontal plane passing through the upper forms the orifice. The cup may be made of thin brass or silver, either hammered or cast, and then turned and polished on a lathe; the diameter being from two to four inches, and the eccentricity of the elliptical figure varied within certain limits according to circumstances. The most convenient proportion, however, is to have this eccentricity equal to half the transverse axis, and, consequently, to place the focus at the third part of the whole height of the cavity, the diameter of the sentient ball being likewise nearly the third part of that of the orifice of the cup. In order to separate more the balls of the pyroscope, the gilt one may be carried somewhat higher than the other, and lodged in the swell of the cavity, its stem being bent to the curve, and the neck partially widened, to prevent the risk of dividing the coloured liquor in carriage. A lid of the same thin unpolished metal as the cup itself is fitted to the mouth of the athrioscope, and only removed when an observation is to be made. The scale may extend to 60 or 70 millesimal degrees above the zero, and about 15 degrees below it.

This instrument exposed to the open air in clear weather will at all times, both during the day and the night, indicate an impression of cold shot downwards from the higher regions. Yet the effect varies exceedingly. It is greatest while the sky has the pure azure hue; it diminishes fast as the atmosphere becomes loaded with spreading clouds; and it is almost extinguished when low fogs settle on the surface. The name Athrioscope (from Athros, serenus, sudus, frigidus) may, therefore, be justly appropriate to this new combination of the pyroscope. The sensibility of the instrument is very striking, for the liquor incessantly falls and rises in the stem with every passing cloud. But the cause of its variations does not always appear so obvious. Under a fine blue sky, the athrioscope will sometimes indicate a cold of 50 millesimal degrees; yet on other days, when the air seems equally bright, the effect is hardly 30°.

Particular winds at different altitudes seem to modify the result, and so perhaps may the transition from summer to winter. Four months are scarcely elapsed since this instrument was first contrived, and during that time very few opportunities have occurred for making nice observations.

The athrioscope might be reduced to a smaller and more compact form, by conjoining with it a pendant differential thermometer. Neither of the glass balls in this case requires to be gilt; but the lower one is encased by a hollow sphere of brass, composed of two pieces which screw together, and the upper ball occupies the focus of the cup, which needs scarcely be more than two inches wide. This variety of the instrument is equally accurate, but, under any change of temperature, rather slower in its action than the former.

On replacing the metallic lid, the effect is entirely extinguished, and the fluid in the stem of the differential thermometer sinks to zero. A cover of pasteboard has at first precisely the same influence; but after it has itself become chilled by this exposure, it produces a small secondary action on the sentient ball, scarcely exceeding, however, the tenth part of the naked impression. A lid of glass or of mica intercepts the impressions like one of paper; for the admission of light has no deranging effect if the athrioscope be rightly constructed and highly polished. The minute secondary action is almost extinguished, if screens of paper, glass, or mica, be held at some distance above the mouth of the instrument.

In the first form of the athrioscope, it is not essential, (though it augments the effect,) that one of the balls should be gilt, since the other being placed naked in the focus receives the pulses much concentrated. If both the balls were formed of black glass, the athrioscopic impressions would evidently be blended with opposite photometrical ones. As long as the action of the light from the sky predominates, the instrument indicates an excess of heat; but after the pulses darted from the higher atmosphere come to prevail, it will mark the excess of cold. The liquor is stationary, when these contending influences are exactly balanced.

To ascertain whether the cold pulses are shot obliquely as well as in the vertical direction, the athrioscope may be constructed to turn towards any portion of the sky. To effect this, the form best adapted for the reflexion would be that of an hyperbola, whose asymptotes have an inclination equal to the visual angle of the space to be explored. But to obtain accurate results, the focal ball must be small, and the hyperbolic conoid wide and much extended. It will answer nearly the same purpose, however, to adopt a truncated spheroid, of great eccentricity: Let the height of the focus, for instance, be one inch, that of the entire cavity nine inches, and, consequently, the widest diameter six inches. The figure on the other side is rather more distended, its extreme width being equal to double the eccentricity, and the focal ball dividing the height of the orifice in the ratio of 1 to $3 + \sqrt{8}$, or 6 to 35 nearly. While that sentient ball remains always in the same position, the axis of the instrument can, by means of a screw acting on the limb of a quadrant, be depressed or elevated to any given angle. But the effect will chiefly be produced by the direct impressions: for the lateral pulses, striking less obliquely against the cavity of the spheroid, will be feebly reflected. This moveable athrioscope was placed in a convenient situation out of doors, when the sky appeared free from clouds, and had assumed a clear blue tint. The spheroid being turned first upright, the effect was noted; but this continued still unchanged, on depressing the axis successively, till it had approached the limit of energetic range, or within 20 degrees of the horizon. From every portion of the sky that subtends a given visual angle, there is hence received the same quantity of the frigorific pulses. But such would likewise be the result, if they were showered from the horizontal surfaces of the successive strata which divide the atmosphere; since although the intensity diminishes in the ratio of the sine of obliquity, a projecting space proportionally broader is for each elemental angle brought into action, as evidently appears from the annexed figure. This entire agreement between theory and observation is most satisfactory.

The same sectoral form of the athriroscope discloses also the peculiar influence of clouds in obstructing the frigorific pulses excited in the atmosphere. When the sky was completely obscured by a dense canopy of clouds, the instrument being pointed to the zenith, marked only five millesimal degrees; but, on lowering it successively to the angle of 30 degrees above the horizon, it continued to indicate still the same effect. Water almost completely absorbs the pulsatory impressions of heat or cold; and may not clouds, consisting of diffuse aqueous particles, produce a similar effect? But the feeble action of five degrees, amounting scarcely to the eighth part of what is observed in clear weather, could not be any remnant of the pulses from the higher celestial regions, which had penetrated through the mass of vapours; because, if the vertical transit, through the obstructing range, allowed only an eighth part to escape, the oblique passage of 30 degrees, redoubling the extent of absorption, would have reduced the final discharge to five-eighths of a degree. The impression measured by the athriroscope, in this case, must therefore have originated wholly in the strata of air between the under surface of the clouds and the ground. But in that narrow space, the extreme difference of temperature would be comparatively small. Hence the frigorific action is found always to diminish as the clouds descend. Nor does their variable denseness appear materially to affect the result, which is often the least, when a very thin, whitish, but low vapour, gathers in the atmosphere. Hence the athriroscope might, with great facility, be employed to estimate the altitude of clouds.

As the higher strata of the atmosphere thus dart Pulses of cold pulses downwards, so the lower strata must evidently project equal pulses of heat upwards. But to measure these, it would require the athriroscope to be inverted and furnished with a pendant pyroscope. The instrument, now carried to the top of a lofty mountain, and directed to the plain below, would indicate a considerable impression of heat, nearly proportional to the quantity of ascent; and, therefore, amounting, for example on the summit of Chimborazo, to perhaps 20 millesimal degrees. But, in the same situation, the common athriroscope might be expected to mark a impression of cold from above, as just so much diminished. No opportunity, however, has yet occurred, on a large scale, for making these interesting observations. A balloon would afford the readiest mode of verifying the theory.

The inverted athriroscope likewise discovers the quality and measure of the pulses projected from the ground. These, in general, are very feeble, seldom in this climate exceeding 3 or 4 degrees. In the progress of a bright day, as the ground grows warmer than the incumbent air, it excites hot pulses; but, as the sun declines, the effect gradually diminishes; till this again returns, increasing with a contrary character, when the surface of the earth has become relatively colder.

The same instrument being suspended a few feet above the ground while the sky appeared clear and blue, a silver tray was laid under it, and the reflected impression of cold amounted to 25 degrees, but, on interposing a plate of glass, it was reduced to 2 degrees; and on removing this, and pouring a sheet of water over the silver, the effect was absolutely extinguished. The absorbent influence of water, and consequently of clouds, was thus distinctly shown.

The nature and intensity of the cold and hot pulses excited in the several strata of the atmosphere, may be easily understood from the annexed figure. Let two equal and opposite circles touch the straight line AB, which divides a stratum of cold from another of warm air. While the diameters CD and cd represent the force of the per- pendicular pulses of cold darted downwards, and of heat upwards, the chords CF, CE, CH, and CG, and Cf, Ce, Ch, and Cg, will likewise exhibit the strength of the pulses which are shot obliquely.

The athrioscope thus opens new scenes to our view. It extends its sensation through indefinite space, and reveals the condition of the remotest atmosphere. Constructed with still greater delicacy, it may perhaps scent the distant winds, and detect the actual temperature of every quarter of the heavens. The impressions of cold which arrive from the north, will probably be found stronger than those received from the south. But the instrument has yet been scarcely tried. We are anxious to compare its indications for the course of a whole year, and still more solicitous to receive its reports from other climates and brighter skies.

But the facts discovered by the athrioscope are nowise at variance with the theory already advanced on the gradation of heat from the equator to the pole, and from the level of the sea to the highest atmosphere. The internal motion of the air, by the agency of opposite currents, still tempers the disparity of the solar impressions; but this effect is likewise accelerated by the vibrations excited from the unequal distribution of heat, and darted through the atmospheric medium with the celerity of sound. Any surface which sends a hot pulse in one direction, must evidently propel a cold pulse of the same intensity in an opposite direction. The existence of such pulsations, therefore, is in perfect unison with the balanced system of aerial currents.

The most recondite principles of harmony are thus disclosed in the constitution of this nether world. But we have left no room for pursuing the details. In clear weather, the cold pulses then showered entire from the heavens will, even during the progress of the day, prevail over the influence of the reflex light, received on the ground, in places which are screened from the direct action of the sun. Hence, at all times, the coolness of a northern exposure. Hence, likewise, the freshness which tempers the night in the saltiest climates, under the expanse of an almost constant azure sky. In our northern latitudes, a canopy of clouds generally screens the ground from the impressions of cold. But, within the arctic circle, the surface of the earth is more effectually protected, by the perpetual fogs which deform those dreary regions, and yet admit the light of day, while they absorb the frigorific pulses, vibrated from the higher atmosphere. Even the ancients had remarked that our clear nights are generally likewise cold. During the absence of the sun, the celestial impressions continue to accumulate, and the ground becomes chilled to the utmost in the morning, at the very moment when that luminary again resumes his powerful sway. But neither cold nor heat has the same effect on a green sward as on a ploughed field, the action being nearly dissipated before it reaches the ground among the multiplied surfaces of the blades of grass. The lowest stratum of air, being chilled by contact with the exposed surface, deposits its moisture, which is either absorbed in-

to the earth, or attracted to the projecting fibres of the plants, on which it settles in the form of dew or hoar frost. Hence the utility in this country of spreading awnings at night, to screen the tender blossoms and the delicate fruits, from the influence of a gelid sky; and hence, likewise, the advantage of covering walled-trees with netting, of which the meshes not only detain the frigorific pulses, but intercept the minute icicles, that, in their formation, rob the air of its cold.

The novelty and importance of the principles which regulate the distribution of heat in the atmosphere seemed to require a full discussion; but we have already outrun the space allotted for this article, and must, for the present, content ourselves with subjoining a few corollaries and general remarks. In a future part of this work we purpose to resume the consideration of the minor branches of the subject of Climate, and with more advantage, certainly, after the experiments and observations, now in progress, shall have come nearer to their conclusion. The relation of air to moisture will be treated under the word Hygrometry, and the complex phenomenon will receive a detailed explication under Meteorology. Some farther views and illustrations may be given under Physical Geography, and other heads. The spontaneous arrangement and succession of the natural families of plants over the surface of the earth, in different latitudes and elevations, would alone form a very interesting article.

From what has been explained, it is easy to perceive, why the climate of an island should have a distinct character from that of a wide continent. The latter will experience a much greater range of heat and cold than the former, though the mean temperature, in like circumstances, will be the same in both. The proximity of the ocean quickly absorbs the inequality of the solar impressions. The passage from summer to winter is hence but feebly marked in detached islands. The prevalence, likewise, in such situations, of a land breeze during the day, and of a sea breeze during the night, especially near the tropics, reduces to very moderate limits the effects produced by the vicissitude of light and darkness.

The coldness of particular situations has very generally been attributed to the influence of piercing winds which blow over elevated tracts of land. This explication, however, is not well founded. It is the altitude of the place itself above the level of the sea, and not that of the general surface of the country, which will mould its temperature. A cold wind, as it descends from the high grounds into the valleys, has its capacity for heat diminished, and, consequently, becomes apparently warmer. The prevalence of northerly above southerly winds may, however, have some slight influence in depressing the temperature of any climate.

It has often been assumed as an incontrovertible fact, that the clearing of the ground, and the extension of agriculture, have a material tendency to ameliorate the character of any climate. But whether the sun's rays be spent on the foliage of the trees, or admitted to the surface of the earth, their accumulated effects in the course of a year, on the incumbent atmosphere, must continue still the same. The direct action of the light would, no doubt, more powerfully warm the ground during the day; if this superior efficacy were not likewise nearly counterbalanced by exposure to the closer sweep of the winds; and the influence of night must again re-establish the general equilibrium of temperature. The drainage of the surface will evidently improve the salubrity of any climate, by removing the stagnant and putrefying water; but it can have no effect whatever in rendering the air milder, since the ground will be left still sufficiently moist for maintaining a continual evaporation to the consequent dissipation of heat.

Much has been said of the comparative low temperature of the American Continent. Its majestic forests, impervious to the solar beams, and its immense lakes, diffusing their vapours, are supposed sufficient to make the climate cold and damp; and the most splendid prospects have been delineated of those changes, which an active, free, and rapidly extending population, is destined to produce in reclaiming that vast region from the rankness of nature, and opening its soil to the genial influence of heaven. Much inaccuracy and exaggeration, however, has prevailed on this subject. The extremes of summer and winter probably differ more in America than in the old world, but the mere temperature on any parallel appears, when carefully taken, to be nearly the same. Thus, Mr Warden (Chorographical Description of the District of Columbia, 1816) found a spring in the vicinity of the capital of the United States, and therefore a little above the level of the sea, to mark 58° in Fahrenheit's scale; but two chalybeate springs in the same quarter, though perhaps deeper seated, showed a heat of 62° and 64°. Chalybeates are not deemed warm springs, or affected by their slight mineral ingredient. But on the same parallel of 39°, the mean temperature of the ancient Continent is 63°.

Since the above was written, the third volume of the Memoires de Physique et de Chimie of the Society of Arcueil has reached us, containing, among other articles, an elaborate paper of the celebrated and accomplished traveller Baron Humboldt, On Isothermal Lines, and the Distribution of Heat over the Globe. Laying aside every theoretical consideration, this distinguished philosopher has here endeavoured to class the results of his own very numerous thermometrical observations with all those which he could collect from different quarters. The first difficulty that occurs is the mode of ascertaining the mean temperature of any place. It was found that half the sum of the maximum and minimum observed during the day and night, or through the summer and the winter, does not represent the true quantity. M. Humboldt has remarked that, between the parallels of 46° and 48°, the thermometer at the moment of sun-setting indicates in every season very nearly the medium temperature of the day. If this fact could be extended to other latitudes, it would greatly abridge the labour of meteorological observations.

From the data employed by M. Humboldt, he calculates that, corresponding to the latitudes of 30°, 40°, 50°, and 60°, the mean temperatures on the west side of the Old Continent are 70°.5, 63°.1, 56°.9, and 40°.6; but, on the east side of the New Continent, only 60°.9, 54°.5, 38°, and 42°.2. The isothermal lines, or lines of equal temperature, under the tropics run across the Atlantic nearly parallel to the equator; but, in the middle latitudes, they bend southerly towards the coast of America. These lines run nearly parallel into the interior of the New Continent, till they pass the Rocky Mountains, after which they bend again northwards. The climate is comparatively mild on the western shore of North America.

It is well known that the difference between the temperature of the winter and of the summer months increases in advancing from the equator to the pole. On the isothermal lines of 68°, 59°, 50°, and 41°, by Fahrenheit's scale, M. Humboldt estimates the extreme range of the year at 22°, 29°, 32°, and 36°, on the Old Continent, and at 27°, 42°, 41°, and 52°, on the New Continent.—But we must now conclude, in the hope of being able to resume this interesting discussion.