THE EVOLUTION OF STELLAR SYSTEMS 85 



luminous bodies, whilst their interiors would be still very hot. 

 Our earth and the inner planets seem to have reached this 

 stage, whilst Jupiter and Saturn appear to be still, to a small 

 extent, self-luminous. Estimates of the past and future duration 

 of our system have been formed by Lord Kelvin, Helmholtz 

 and others ; but the very various lengths of time given, ranging 

 from twenty to four hundred millions of years, alone show that 

 these periods are little more than rough guesses, needing further 

 knowledge to be of value. The discovery of the properties of 

 radium has enormously extended the probable future duration 

 of the sun's heat. " We have every reason to think," says 

 Arrhenius, " that the sun's chemical energy will suffice to 

 maintain its heat during thousands of millions, perhaps billions 

 of years." 



In 1861 Babinet proposed the application of a criterion, based 

 on the mechanical principle of the "conservation of areas." He 

 showed that if w be the sun's angular velocity of rotation, with 

 radius r, and w r' represent these quantities when the globe is 

 expanded so as to have the radius r\ then 



cor' = w'r' ""' [Moment of momentum, a constant quantity for a system 

 rotating freely and subject to no external forces] 

 or 



C = Inir^di = oo^/nr^ = w'Swr^ ^. 



Suppose now the "solar nebula" extending to the earth's orbit, 

 let us find its time of rotation. We get for this 



25'3 days f "3^445 j _ ^^igzjears. 



For the case of Neptune, whose mean distance is thirty times 

 that of the earth from the sun, the solar nebula when reaching 

 to that distance will rotate in 



25-3 days (32^^M45y ^ 3^888,533 years. 



(These figures are taken from a paper by Dr. See.) 



Applying this criterion to the case of the various planets 

 and satellites of our system, we find periods in every case much 

 greater than the known periods of revolution of these bodies. 

 The earth revolves in one year about the sun, Neptune in 

 about a hundred and sixty-five years. Thus it follows that 

 the "hypothetical solar nebula could not have rotated with 



