The general causes of the temperature of the globe are the radiation of the sun, and the proper heat of the earth and its radiation ; their effects however are greatly modified by various local circumstances, such as the vicinity of seas or mountains, and the difference in radiating lower of the soil, together with the conducting powers of the strata subjacent to the particular places, with other causes less permanent.
With respect to the proper heat of the earth, we observe in any latitude that at a depth which is very small compared with the radius of the globe, the temperature is permanent throughout the year, the ellisets of solar radiation being confined to a superficial stratum of inconsiderable thickness This fact has been fully established by lung continued obeervationa in the cellars of the Obser• eatery at l'aria, and by observations in the mines of Cornwall, in Scotland, and in other countries. if this stratum be supposed to be gripped elf, the internal nucleus may be considered as nearly a spherical mass, arrived at a permanent state of temperature in each part, and subject at its external surface to a given distribution of heat, or to a given power of exterior conductibility. The depth at which this permanence of temperature occurs is different in different lati tudes, inasmuch as the solar action on the superior stratum is also different on account of the greater or less obliquity of its rays, and likewise on account of the earth's elliptic annual motion. Thus we have the following observed relations between the permanent tempera tures and the corresponding latitudes :— where v represents the temperature at a point of which the rectangular co-ordinates are x, y, z, and the constant K depends on the interior conducting power, and t is the time. In the case of a sphere with a radius n, we may place the origin of co-ordinates at the centre, and transforming the above from rectangular to polar co-ordinates (namely, r, the distance from the centre, 0 the angle formed by the radius vector with an axis, and ˘ the inclination of the plane of 0 to one of the co ordinate planes, the angles necessarily disappear from the transformed equation, and) it becomes must proceed according to some even power of the latitude in order to amount to the same quantity in equal latitudes north and south, for which reason he chose the least even positive power of the sine. How ever, since the quantity of land in the northern hemisphere is about three times as great as in the southern, the solar heat accumulates more in the former, and in the latter is more eqbablo between winter and summer. Sir D. Brewster has substituted for Mayer's the formula t = 81'50 cos L, which bears an exceedingly good comparison with observations, but for the reasons above given lie has found it necessary to modify it for the New World. Mr. Atkinson has shown that the mean of the errors of Mayer's and Brewster's formula; for ten places nearly on the level of the sea are respectively + 1°•72 and — •12.
The temperatures of April and October are generally nearly the mean of the year, which also is found to vary but little in a considerable suc cession of years. If T be the mean temperature at an altitude h in feet, in a given place where t is the temperature of the surface, to express T, Mr. Atkinson has proposed the formula T= t — , giving for the 251 + 200 extreme atmospheric cold the temperature — 200°, which is probably near the truth.
The names of Isotheral, Isocheimal, and Isothermal lines have been given to lines passing through places which have equal mean summer, winter, or annual temperatures, the two former having contrary courses, and the third intermediate. The difference of latitude between places in the New and Old Worlds, on the same isothermal line, is consider able, as appears from the following table :— on the supposition that the exterior permanent temperatures were uniform; to which we must annex the following equation for the dv surface, + h (v — a) = 0, where a represents the temperature of the medium in contact with the globe, and h the index of exterior conductibility of the globe. But in the Case of the earth both K and It are variable, and the former must then be brought under the sign of differentiation. After there shall have been a greater number of observations on the permanent interior temperatures of the earth, the above equations will be very useful in enabling us to calculate the temperatures at depths under the surface greater than it is probable min can ever penetrate, and they will assist in the explanation of the numerous phenomena which depend on the internal heat of various parts of the globe, as volcanoes, thermal springs, &c. Regarding the interior parts which are sufficiently remote 'from the surface as in a dv state of permanent temperature, we should have = 0; when preceding equations admit of easy integration on the supposition that 15 is constant, and of approximate solutions on a probable form of the f unction K when variable. [REFRIGERATION OF TILE GLOBE, and TEMPERATURE, TERRESTRIAL, DISTRIDU'TION OF.] With respect to the heat of the external stratum, it is principally dependent on the radiation of the sun, the effect of which depends on the duration and the obliquity of the solar rays, both of .which are dependent on the declination of the sun and the latitude of the place. The integral taken throughout the year depends therefore solely on the latitude : from this integral the calculated mean temperature is derived, but differs in most cases from the observed inasmuch as the propagation of heat in the sea and in the air affects unequally those places in the same parallel which are near to or distant from the coasts, and the unequal quantity of continent in the northern and southern hemispheres produces a similar result with respect to them.