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.