Abstract
THE statement quoted by Mr. Fisher from Dr. Croll (NATURE, vol. xx. p. 577) that “the temperature of a place, other things being equal, is proportional to the heat received from the sun,” is based on the assumption of Newton's law of cooling, viz., that the rate of cooling of a body is proportional to the excess of its temperature above that of the surrounding medium. This is approximately true only when the excess is small. When the excess becomes large the rate of cooling augments much more than in proportion. The amount of heat which must be supplied to a body in order to maintain it above the temperature of the surrounding medium is proportional to what would be its rate of cooling. Hence this amount increases as the excess of temperature increases—proportionally while the excess remains small, but much more than proportionally when it becomes large. Conversely, the temperature increases more slowly than the amount of heat supplied, and any variation in the supply will affect the temperature produced in a degree which is less for a large excess than for a small one, and, therefore, less than Newton's rule would give. The excess of the earth's mean temperature above that of space is large, and consequently calculations of changes based on Newton's rule must be in excess of the truth.
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HlLL, E. [Letters to Editor]. Nature 20, 626 (1879). https://doi.org/10.1038/020626b0
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DOI: https://doi.org/10.1038/020626b0
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