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Theoretical Researches on the Daily Change of the Temperature of the Air

Published online by Cambridge University Press:  15 September 2014

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I have the honour to lay before the Royal Society a short account of some theoretical researches on the daily change of the temperature of the air, made by me in 1895, and published to a certain extent in the Nova Acta der kaiserlich Leopoldinisch-Carolinischen Academie der Naturforscher, Band lxvii., No. 2. Some more recent investigations on the subject, chiefly dealing with the physical point of view of the problem, have not yet been published, but seem to me of such importance as to justify me in presenting a brief sketch of them to the Society in this paper.

The history of the mathematical aspect of the problem can be traced back as far as the middle of the last century, when Lambert made the first attempt at investigating the relation between solar and terrestrial radiation and the temperature of the atmosphere. He was succeeded by a great number of famous mathematicians and meteorologists, whose labours, however, though they contributed considerably to our knowledge of certain parts of the question, have not been rewarded, it must be said, with any sufficient result; so that a satisfactory solution of the problem by means of theoretical investigations has been eventually considered impossible, at least in some quarters.

There can be no doubt that, in a problem like this, an immense number of different errors affect the principal conditions of the propagation of heat, which conditions are supposed to be the causes of the observed changes of the temperature.

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Proceedings
Copyright
Copyright © Royal Society of Edinburgh 1897

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References

page 260 note * This formula obviously includes the case of conduction between the soil and the fiist elements of the atmosphere too—provided we make no assumptions on the nature of the function ϕ(λ). If, in what follows, we simply speak of radiation between soil and air, we always tacitly refer to the piobable existence of such conduction.

page 269 note * Researches on Solar Heat and its Absorption by the Earth's Atmosphere. A Eeport of the Mount Whitney Expedition.

page 271 note * I have to correct a mistake in this part of the paper already published, caused by an erroneous theoretical consideration, which, however, does not alter the result derived from the integral.

At stations where the thermometer is too much protected by houses, etc., and where the sun's rays have not sufficient access to the neighbouring ground, we generally observe a diminution of the daily range connected with a retardation of the time of maximum temperature. It is not difficult to find the cause of these phenomena—first, in the diminution of solar radiation acting upon the neighbouring soil; and, secondly, in the continuous currents of hotter air, which are caused by the upward direction of the currents on the roofs of the houses, and which mix with the colder air near the protected position of the thermometer. Hence we have to alter the above equations by taking a smaller value of K, and changing the sign of the expression dk cos (ζ – ν′). On a much larger scale the same phenomenon appears in mountainous countries, where currents of heated air flowing up a valley during day-time give the same peculiar character to the daily curve of its temperature.

page 274 note * Supplementband zum Repertorium für Meteorologie, St Petersburg, 1881Google Scholar.