286 The Origin and Evolution of the Solar System [CH. xn 



they have moved several times across the universe before becoming so 

 evenly arranged as they now are. For example, the assumption that each 

 star has made ten journeys to-and-fro would give an age of the order of 

 3,200,000,000 years. 



Here we have three more or less conjectural estimates differing, roughly 

 speaking, by successive powers of 10. The last and largest estimate, being 

 most closely allied to the subjects we have been discussing, may be con- 

 sidered first. 



307. The estimate implicitly assumes that the period of motion across or 

 round our universe has always been the same as now. Our investigations, on 

 the contrary, have led us to conjecture that our system of stars may have 

 only recently expanded to its present size ; we have even found reasons for 

 supposing that the expansion is not yet finished. If we estimate the age in 

 terms of its completed orbits among the other stars, it is true that the last 

 orbit is now being performed at the rate of one revolution (say) per 320,000,000 

 years, but the first orbit may, we have supposed, have been completed in 

 160,000 years. The time often orbits will not be ten times 320 million years; it 

 will be more nearly equal to the sum of ten terms of a geometrical progression 

 beginning with 160,000 years and ending with 320 million years; this sum 

 is 560 million years. Considering the uncertainty of all the numerical data, 

 this estimate may be considered to be in agreement with the geological 

 estimate, the estimate of 560 million years referring to the time since the 

 primaeval rotating nebula begun to break up into stars, and the geological 

 estimate of 250 million years referring to the period since the earth solidified. 



308. The only discordant estimate is seen to be that derived from the 

 sun's radiation. Taking the solar constant to be T92, the sun radiates away 

 3 '8 x 10 33 ergs per second. The gravitational energy gained by the sun in con- 

 tracting to a homogeneous mass of its present size is 2*2 x 10 48 ergs, representing 

 radiation for 18*3 million years at the present rate. It hardly appears probable 

 that the sun can have other sources of energy comparable with its gravitational 

 energy. Chemical energy is well known to be insignificant. Lindemann* has 

 pointed out that radioactive energy will also be insignificant in comparison 

 with gravitational. It is possible that other sub-atomic changes, unknown to 

 us, may provide more energy than radioactive changes. If these changes con- 

 sist of a mere rearrangement of electrons, it is found f that each electron in the 

 sun would have to fall through a sub-atomic difference of potential equal- to 

 3000 volts in order to set free as much energy as that set free by gravitational 

 contraction, so that the possibility of extending the time-scale in this way 

 seems remote. There remains, apparently as a last resource, the possibility of 

 energy being created by the destruction of matter, as for instance by positive 



* Nature, April 22, 1915. 



f J. H. Jeans, Nature, August 2, 1917. 



