Let us suppose that the crusts of the sun and the earth have the same thermal conductivity—namely, that of granite. According to Homén, a slab of granite one centimetre in thickness, whose two surfaces are at a temperature difference of 1° Cent., will permit 0.582 calorie to pass per minute per square centimetre of surface. By analogy, the earth’s crust, with an increase of temperature of 30° per kilometre, as we penetrate inward, would allow 1.75 .10^{-4} calorie to pass per minute and per square centimetre (this is 1/3580 of the mean heat supply of the earth, 0.625 calorie per minute per square centimetre); while the sun, with a crust of the same thickness as the earth, but with a diameter 108.6 times larger, would lose 3.3 times more heat per minute than the earth receives from it at the present time. At present the sun loses 2260 million times more heat than the earth receives; consequently, the loss of heat would be reduced to 1/686,000,000 of the present amount. If the thickness of the solar crust amounted to 1/140 of the solar radius—that is to say, to the same fraction that the thickness of the earth’s crust represents of the terrestrial radius—the sun would in 74,500 million years not lose any more heat than it does now in a single year. This number has to be diminished, on account of the colder surface which the sun would have by that time, to about 60,000 million years. Considering that the mean temperature of the sun may be as high as 5 million degrees Celsius, the cooling down to the freezing-point of water might occupy 150,000 billion years, assuming that its mean specific heat is as great as that of water. During this time the crust of the sun would increase in thickness and the cooling would, of course, proceed at a decreasing rate. In any case, the total loss of energy during a period of a thousand billion years could, under these circumstances, only constitute a very small fraction of the total stored energy.