ASTRONOMY 355 



Mathematics, Geology, Zoology and Botany. Previous refer- 

 ences in these notes to this subject will be found in Science 

 Progress, 10, 281, 191 5-16, and 14, 553, 1920 (" The Sources 

 of Stellar Energy "). The inadequacy of Lord Kelvin's original 

 estimate of twenty or thirty million years has long been 

 admitted. His estimate was arrived at in three different ways. 

 But the argument from the temperature gradient inside the 

 earth's crust has been invalidated by the discovery of radio- 

 activity. In fact, Lord Rayleigh, in the discussion at the 

 British Association, stated that if we suppose the radium content 

 found in the superficial layers of the earth to extend for twenty 

 miles downwards the whole output of heat from the earth 

 can be accounted for without assuming the existence of the 

 primeval store of energy which was postulated by Lord Kelvin. 

 The existing state of things cannot be used as a firm basis from 

 which to explore the past. 



As regards the sun's heat, radio-activity cannot explain its 

 maintenance, and gravitational contraction is not sufficient. 

 The giant red stars radiate heat at something like 1,000 times 

 the rate at which the sun does, and the contraction theory alone 

 is inadequate to explain their present existence. Some other 

 source of stellar energy must be postulated. Prof. Eddington 

 pointed out that if the radiation of 8 Cephei was derived from 

 gravitational contraction, the density must increase i per cent, 

 in forty years. This star is a variable, whose variation is 

 believed to be due to periodic pulsations. A change of density 

 must therefore be accompanied by a change of the period of 

 pulsation. In the case of S Cephei the change of period is known 

 with some accuracy to be only o-o8 seconds per annum, or i 

 per cent, in 58,000 years, corresponding to a change of density 

 of I per cent, in 29,000 years. It follows that the star has 

 sources of energy other than gravitational, and that Lord 

 Kelvin's time-scale must be increased in a ratio of about 29,000 

 to 40, or 700 to I . In the case of the sun, which is a dwarf star, 

 and farther advanced in its evolution, a smaller — though still 

 large^ — factor would be required. Kelvin's argument from the 

 heat of the sun is therefore invalid. 



Lord Rayleigh considers that the most accurate estimate of 

 the age of the earth can be derived from the rate of radio-active 

 disintegration. Uranium passes through a series of successive 

 stages during its disintegration which terminate in an isotope 

 of lead, having an atomic weight less than that of " ordinary " 

 lead, but chemically indistinguishable from it. The order and 

 rate of this disintegration through successive stages are known 

 with a high degree of accuracy, so that a determ.ination of the 

 amount of the isotope of lead present in minerals containing 

 uranium enables the time when disintegration commenced to 



