The most inattentive observer of the phenomena of nature must have noticed, that there are considerable variations in the temperature of the air in any parti cular place, exclusive of the differences of seasons and climates, which eternal changes cannot be produced by heat de rived from the sun, as its rays concen trated have no kind of effect on air; those however heat the surface of our globe, which is communicated to the im mediate atmosphere ; it is through this fact that the temperature is highest where the place is so situated as to receive with most effect the rays of the sun, and that it varies in each region with the season ; it is also the cause why it decreases in proportion to the height of the air above the surface of the earth. The most per pendicular rays falling on the globe at the equator, there the heat of it is the greatest, and that heat decreases gradu ally to the poles; of course the tempera ture of the air is in exact unison ; from this it appears, that the air acquires the greatest degree of warmth over the equa tor, whence it becomes insensibly cooler till we arrive at the poles: in the same manner, the air immediately above the equator cools gradually. Though the temperature sinks as it approaches the pole, and is highest at the equator, yet, as it varies continually with the seasons, it is impossible to form an accurate idea of the progression, without forming a mean temperature for a year, from that of the temperature of every degree of latitude for every day of the year, which may be accomplished by adding together the whole of the observations, and divid ing by their number, when the quotient will be the mean temperature for the year. "The diminution," says Dr. Thom. son, the pole to the equator takes place in arithmetical progression ; or, to speak more properly, the annual tempe rature of all the latitudes are arithmeti cal means between the mean annual tem perature of the equator and the pole." Mr. Mayer has the honour of this disco very, but Mr. Kirwan rendered it more simple and plain, by founding an equation on it, by which he calculated the annual mean temperature of every degree of latitude between the equator and the pole ; the following was the principal of proceeding : "Let the mean annual heat at the equator be in, and at the pole ea—en ; put o for any other lititude ; the mean annual temperature of that lati tude will be m — n X If there fore the temperature of any two latitudes be known, the value of m and n may be found. Now the temperature of north lat. 40° has been found by the best ob servations to be 62.1°, and that of lat. 50°, 52.9°. The square of the sine of 40° is nearly 0.419, and the square of the sine of 50° is nearly 0.586. Therefore, In— 0.41 n = 62.1, and m — 0.58 ri = 52.9, therefore 62.1 + 0.41 u = 52.9 + 0.58 ti as each of them from the two equations is equal to en. From this last equation the value of 71 is found to be 53 nearly ; and m is nearly equal to 84. The mean tempera ture of the equator, therefore, is 84°, and that of the pole to 31°. To find the mean temperature for every other lati tude, we have only to find 88 arithmeti cal means between 84 and 31." Mr. Kirwan calculated a table of the mean annual temperature of the stand ard, situated in every latitude, which an swers only for those of the atmosphere of the ocean, as it was made for that part of the Atlantic situated between 80° north and 45° south latitude, extending westward to the gulf stream, within a few leagues of the American coast ; and for all that part of the Pacific Ocean, from the 45th degree of northern to the 40th of southern latitude, from the 20th to the 275th degree of longitude east of Lon don. Mr. Kirwan terms this part of the ocean the standard, as the rest is sub ject to anomalies to be mentioned here after. The same industrious gentle man ascertained the monthly mean tem perature of the standard ocean ; that of April approaches very nearly to the an nual mean, "and as far as heat depends on the action of solar rays, that of each month is as the mean altitude of the sun, orrather as the sine of the sun's altitude." The learned investigators, to whom we are indebted for these experiments and observations, say, "As the sine of the sun's mean altitude in April is to the mean heat of April, so is the sine of the sun's mean altitude in May to the mean heat of May. In the same manner the mean heats of June, July, and August, are found ; but the rule would give the temperature of the succeeding months too low, because it does not take in the heat derived from the earth, which pos sesses a degree of heat nearly equal to the mean annual temperature. The real temperature of these months, therefore, must be looked upon as an arithmetical mean between the astronomical and ter restrial heats. Thus, in latitude 51°, the astronomical heat of the month of Sep tember is 44.6°, and the mean annual heat is 52.4 ; therefore the real heat of 44.6+52 2 .4 this month should be---= 48.5.
After many laborious calculations, Mr. Kirwan had the mortification to find their results differed so much from observa tions, that he was induced to make a ta ble from various sea journals, and certain principles, for the monthly mean tempe rature of the standard, from lat. 80° to
lat. 10°, from which he decides, that the coldest month in every latitude is Janua ry, and that July is the warmest in all above 48° ; in lower, August. In propor tion to the distances from the equator is the increase and decrease of heat, but every latitude where existence can be maintained has a mean of 60°, two months of the year at the least, which is requisite for the production of those articles by which man supports life. The tempera tures within ten degrees of the poles va ry little, and the case is similar within the same distance from the equator; those of different years near the latter differ very little, but the differencesincrease as the latitudes approach the poles. It is well known that the temperature of the atmosphere diminishes gradually in pro portion to its height above the level of the sea. The late Dr. Hutton of Edin burgh made some experiments on this head, by placing a thermometer on the summit of Arthur's Seat, a hill so named, and another at the base of it, by which he found that the former generally stood at three degrees lower than the latter; in this instance therefore a height estimated at 800 feet produced a diminu tion of heat amounting to three degrees. Bouguer made a similar experiment, to ascertain the difference oftemperatu re be tween the level of the sea and the top of Pinchinca,one oftheAndes,wben the thee mometer at the summit stood at 30°, and that below in the same latitude at 84° ; the diminution was 54° in a supposed height of 15,564feet. Thus far the operation is easy and practicable, but the grand diffi culty lies in determining the exact grada tions between the highest and lowest points of observation ; conjectures on this subject have been hazarded by Euler and Saussure ; the first gives it in harmonic progression, and Saussure supposed the decrease of temperature to amount to 1° for 287 feet of ascent. Mr. Kirwan, however, rejecting those improbabilities, shows, in the Transactions of the Royal Irish Academy, that the rate of diminu tion depends upon the precise tempera ture of the surface of the earth where an experiment is made ; he has besides invented an ingenious mode of ascer taining the rate in every instance, admit ting the temperature at the surface to be known.
This gradual approach to cold demon strates, that at a certain height eternal congelation must prevail; that height va ries of course according to the latitude of the place, being highest at the equa tor, and gradually descending on ap proaching the poles; it is also lower in the winter. The cold on the summit of Pinchinca was found, by M. Bouguer, to extend from seven to nine degrees every morning, previous to the rising of the sun, below the freezing point, from which he conjectured, that the mean height of the term of congelation (or that region where water congeals on some part of every day in the year) between the tropics, is 15,577 feet above the level of the sea; in latitude 28°, he supposes it to be 13,540 during summer; taking the dif ference between the freezing point and the equator, it plainly appears, that it bears the same proportion to the term of congelation at the equator, that the dif ference between the mean temperature of any other degree of latitude, and the freezing point, bears to the term of eon gelation in that latitude." "Thus," con tinues Dr. Thomson, "the mean heat of the equator being 84°, the difference be tween it and 32 is 52 ; the mean heat of latitude 28° is 72.3°, the difference be tween which and 32 is 40.3. Then 52: 15,577 : : 40.3 Mr. Kirwan calcu lated another table on this subject, from latitude 0, where he makes the mean height of the term of congelation 15,577, by gradations of five degrees, up to lati. tude 80-120 feet ; higher than this, call ed the lower term of congelation, which varies with circumstances and seasons,M. Bouguer places another, called by him the upper terni,and beyond this no visible vapour ascends. The former gentleman supposes this line far less liable to varia tion in the summer than in the lower term, and therefore adopted it to ascertain the rate of diminution of heat on ascending into the atmosphere. Bouguer determin ed the height ofthis term in one instance, but Kirivan went further, and produced a table of its height for every degree of la titude in the northern hemisphere. We shall quote Mr. Kirwan's rule for obtain ing the temperature at any given height, admitting that the temperature at the surface of the earth is known. "Let the observed temperature at the surface of the earth be ta, the height given =eh, and the height of the upper term of con gelation for the given latitude be =i t ; tv,-32 then = the diminution of tem 100 1 perature for every 100 feet of elevation ; or it is the common difference of the terms of the progression required. Let this common difference thus found be de noted by c, then c gives us the whole diminution of temperature from the surface of the earth to the given height. Let this diminution be denoted by d, then m—dis obviously the temper ature required. An example will make this rule sufficiently obvious. In latitude 56°, the heat below being 54°, required the temperature of the air at the height of 803 feet.