Two years ago I communicated a short paper on Solar Radiation and Earth Temperatures (Proc, vol. xxiii., pp. 296–311). This paper had its origin in a critical discussion of certain results deduced by Dr Buchan from observations of Mediterranean temperatures which had been made by the staff of the Austrian warship Pola. The mathematical method by which I discussed the relation between the solar energy incident on the surface of earth or sea, and the corresponding fluctuations of temperature in the rock of the Calton Hill and the surface waters of the Mediterranean, has attracted some attention in America; and correspondence with Professor Cleveland Abbe has drawn my attention again to the subject. In this paper I propose to consider more carefully the significance of the observations made and published by the Austrians. These are contained in four quarto volumes, which Dr Buchan has kindly placed in my hands for the purposes of a thorough investigation from the point of view of solar radiation. Dr Buchan clearly saw that something might be made out of these; and the results he gave two and a half years ago before the Society indicated a penetration of solar heat every day to a depth of more than 100 feet. The results were based upon means of temperature at different depths grouped according to the time of day at which they were taken. As I showed in my former paper, the results so deduced indicated a daily penetration into the waters of the Mediterranean of an amount of heat greater than the sun could supply.