1909.] SEE— THE PAST HISTORY OF THE EARTH. 121 



reserved for Babinet of Paris to point out^ a rigorous mechanical 

 law which enables the mathematician to test the nebular hypothesis. 

 Nevertheless, Laplace himself constantly uses the same principle, in 

 the law of the conservation of areas, thoug-h he does not apply it to 

 the development of our system. The principle involved is that of 

 the constancy of the moment of momentum of axial rotation. Ac- 

 cording to this law, we have 



C = ^mr^(o = (o^inr^ = (o'^mr", ( i) 



where r is the radius of the rotating globe, w the angular velocity of 

 rotation, and C a constant ; while / and w' are the corresponding 

 quantities at some other epoch. Thus at any two epochs, however 

 much the freely rotating globe may have changed by contraction or 

 expansion, we always have 



w'r''^ojr-. (2) 



By taking accurate values of the radii and rotation-periods of 

 the sun and planets as now observed, we may calculate the corre- 

 sponding rotation-periods when the globes are imagined expanded 

 to fill the orbits of the planets and satellites. The accompanying 

 table gives the most important data for the solar system. - 



It will be found from this table that the sun would have rotated 

 with extreme slowness if it had been expanded to the orbits of the 

 several planets, and the planets also would have rotated very slowly 

 if they had been expanded to fill the orbits of their satellites. 

 The difiference between the observed periods of revolution and the 

 calculated periods of rotation is so great that we readily see that the 

 planets could never have been detached from the sun, and the satel- 

 lites could never have been detached from the planets, by accelera- 

 tion of rotation as imagined by Laplace. It is evident, therefore, 

 that all of these bodies have been captured or added from without, 

 and have had their orbits reduced in size and rounded up under the 

 secular action of the nebular resisting medium formerly pervading 

 the planetary system. 



Ever since the time of Laplace it has been believed that our 



^Comptes Rendiis, Tome 52, p. 481, March 18, 1861. 

 * Cf. Astron. Nachr., no. 4308. 



