Page:Scientific Memoirs, Vol. 1 (1837).djvu/149

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M. POISSON ON THE MATHEMATICAL THEORY OF HEAT.
137

The mean of the annual temperatures, marked by a thermometer exposed in the open air and in the shade, forms the climateric temperature. It varies with the elevation of places above the level of the sea, and with the longitude and latitude, according to unknown laws. At Paris it is 10°·822, as M. Bouvard has concluded after 29 years of observations. There will be found in this Chapter a table of the mean temperatures for the twelve months of each of those years, which that gentleman has been pleased to communicate to us, and which had not before been published. It appears that in every point of the earth this climateric temperature differs very little from the mean temperature of the surface of the soil, as is shown by several examples. Notwithstanding, the variable temperature of this surface, and that which is marked at the same instant by a thermometer as little elevated above the surface as may be, are often very different from each other; it hence follows, that in a year the excess of the highest above the lowest temperature of the soil is at Paris nearly 24°, as will be seen in the course of this Chapter; and only about 17° for the thermometer suspended in the air and in the shade.

We now determine the part of exterior temperature which results from the atmospherical heat combined with sidereal heat. The necessary data for calculating its numerical value, à priori, being unknown to us, we show how this value, for every point of the globe, may be deduced from the mean temperature of its surface. At Paris this exterior temperature is 13°. Although we cannot determine separately the portion of this temperature of the earth which arises from the atmospherical heat, there is reason to think that it is also negative, so that the other portion arising from sidereal heat must be less than 13° below zero. If we suppose that radiant heat emanating from the stars falls in the same quantity on all points of the globe, this temperature, higher than 13°, will be that of space at the place where the earth is at this time. Without being able to assign the degree of heat of space, we may however admit, that its temperature differs little from zero, instead of being, as had been asserted, below the temperature of the coldest regions in the globe, and even of the freezing-point of mercury. As to the central temperature of the whole mass of the earth, even supposing its original heat to be entirely dissipated, and that it is no longer equal to the present temperature of space, we have no means of obtaining a knowledge of it.

According to a theorem of Lambert, the whole amount of solar heat which falls upon the earth is the same during different seasons, notwithstanding the inequality of their lengths, which is found to be compensated by that of the distances from the sun to the earth. This quantity of heat varies in the inverse ratio of the parameter of the ellipse described by the earth; it also varies with the obliquity of the ecliptic;