gravitation. On introducing numerical values for the symbols in this formula, I find the lost energy to be 2·7 × 10^7 M calories where M is expressed in grams. If we adopt Langley's value of the solar constant, this heat suffices to give a supply for 12 million years. Lord Kelvin used Pouillet's value for that constant, but if he had been able to use Langley's, his 100 million would have been reduced to 60 million. The discrepancy between my results of 12 million and his of 60 million is explained by a conjectural augmentation of the lost energy to allow for the concentration of the solar mass towards its central parts." Now it has been shown (section 266) that one gram of radium emits during its life an amount of heat corresponding to 1·6 × 10^9 gram-calories. It has also been pointed out that there is every reason to suppose that a similar amount of energy is resident in the chemical atoms of the inactive elements. It is not improbable that, at the enormous temperature of the sun, the breaking up of the elements into simpler forms may be taking place at a more rapid rate than on the earth. If the energy resident in the atoms of the elements is thus available, the time during which the sun may continue to emit heat at the present rate may be at least 50 times longer than the value computed from dynamical data.
Similar considerations apply to the question of the age of the earth. A full discussion of the probable age of the earth, computed from its secular cooling from a molten mass, is given by Lord Kelvin in Appendix D of Thomson and Tait's Natural Philosophy. He has there shown that about 100 million years after the earth was a molten mass, the gradual cooling due to radiation from its surface would account for the average temperature gradient of 1/50° F. per foot, observed to-day near the earth's surface.
Some considerations will now be discussed which point to the probability that the present temperature gradient observed in the earth cannot be used as a guide to estimate the length of time that has elapsed since the earth has been at a temperature capable of supporting animal and vegetable life; for it will be shown that probably there is sufficient radio-active matter on the earth to supply as much heat to the earth as is lost by radiation from its surface. Taking the average conductivity K of the materials of
