rate of emission of energy.
An examination of the spectrum of the sun has not so far revealed any of the radium lines. It is known, however, from spectroscopic evidence that helium is present, and this indirectly suggests the existence of radio-active matter also. It can readily be shown49 that the absence of penetrating rays from the sun at the surface of the earth does not imply that the radio-elements are not present in the sun. Even if the sun were composed of pure radium, it would hardly be expected that the γ rays emitted would be appreciable at the surface of the earth, since the rays would be almost completely absorbed in passing through the atmosphere, which corresponds to a thickness of 76 centimetres of mercury.
In the Appendix E of Thomson and Tait’s Natural Philosophy, Lord Kelvin has calculated the energy lost in the concentration of the sun from a condition of infinite dispersion, and concludes that it seems “on the whole probable that the sun has not illuminated the earth for 100,000,000 years and almost certain that he has not done so for 500,000,000 years. As for the future we may say, with equal certainty, that inhabitants of the earth cannot continue to enjoy the light and heat essential to their life for many million years longer, unless sources now unknown to us are prepared in the great storehouses of creation.”
The discovery that a small mass of a substance like radium can emit spontaneously an enormous quantity of heat renders it possible that this estimate of the age of the sun’s heat may be much increased. In a letter to Nature (Sept. 24, 1903) G. H. Darwin drew attention to this probability, and at the same time pointed out that, on Kelvin’s hypotheses, his estimate of the duration of the sun’s heat was probably much too high, and stated that, “The lost energy of the sun, supposed to be a homogeneous sphere of mass M and radius a, is (⅗)μM2/a where μ is the constant of gravitation. On introducing numerical values for the symbols in this formula, I find the lost energy to be 2·7 × 107 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 × 109 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