290 
THE SOURCE OF STELLAR ENERGY 
according as we neglect or allow for reduced radiation in the past. These 
figures are subject to a considerable deduction already mentioned on 
account of ionisation energy, so that 20,000,000 years is probably a 
generous estimate of the sun’s age on the contraction hypothesis. 
202. Biological, geological, physical and astronomical arguments all 
lead to the conclusion that this age is much too low and that the time-scale 
given by the contraction hypothesis must somehow be extended. The 
most direct evidence is given by the determination of the date of formation 
of terrestrial rocks containing radio-active minerals from the uranium- 
helium or the uranium-lead ratio of their contents. In this way an age of 
1300 million years has been assigned to the oldest sedimentary rocks*. 
The sun must be still older and its age can scarcely be put at less than 
10 10 years. 
The rapidity of evolution required by the contraction hypothesis is 
most startling when we consider the giant stars. A star of mass 1T5 
would take 31,000 years to develop from type M (3000°) to type G (6000°) 
and 72,000 years from type M to type A (10,500°); moreover, these figures 
are subject to deduction on account of ionisation energy. 
The Cepheid variables afford direct astronomical evidence against so 
rapid an evolution. From the numerical results for 8 Cephei given in 
§ 134 it will be found that G must increase by 1 part in 40,000 per year 
in order that the balance il — K — H may be sufficient to supply the 
radiation. The radius must accordingly decrease by 1 part in 40,000 and 
the density increase by 1 part in 13,000. Since II Vp i s approximately 
constant the period must decrease by 1 in 26,000 or 17 seconds 
annually. 
The star has been under observation since 1785 and it is impossible 
that so large a change of period could escape detection. It is doubtful 
whether there has been any change at all, the observations since 1848 
being consistent with a uniform period. E. Hertzsprungf finds an annual 
decrease of 0 S T06 ± 0 S -011, the result depending almost entirely on the 
trustworthiness of observations by Goodricke and Pigott in 1785. In any 
case the rate of evolution of 8 Cephei is not more than of that given 
by the contraction hypothesis. There are many other Cepheids which 
should have shown the large change of period if it had occurred, but the 
evidence is always negative. 
* For an account of these and other methods see H. Jeffreys, The Earth, Chapter v. 
On the other hand, arguments by J. Joly, The Surface-History of the Earth, Chapter ix, 
in favour of a lower estimate seem entitled to considerable weight; but even the 
lowest estimates are much too great for the contraction hypothesis. 
f Observatory, 42, p. 338. [Results depending on recent spectrographic observa 
tions have been communicated to me by F. S. Jacobsen. These show the period of 
8 Cephei to be decreasing 0 s -39 annually, and of rj Aquilae increasing 0 s -96 annually.]