THE ORIGIN OF THE EARTH. 11 



Phobos was detached. To explain this difficulty, G. H. Darwin has 

 suggested that tidal retardation may have decreased the planet's rota- 

 tion much more than the contraction increased it, but this seems 

 highly improbable. Furthermore, Moult on has shown that the par- 

 ticles that make, up the inner edge of the inner ring of Saturn revolve 

 in about half the planet's time of rotation, and that the tidal argu- 

 ment, applied to Mars, does not fit this even more singular case with- 

 out making new and inconsistent assumptions. 1 



(6) But perhaps the most severe test to which the Laplacian 

 hypothesis has recently been subjected is founded on a study of 

 the relations of mass and momenta. It is a firmly established law of 

 mechanics that the moment of momentum of any freely rotating or 

 revolving system, like the nebula in question, remains constant, if not 

 influenced from without, whatever changes the system may undergo ; 

 and this principle is peculiarly well adapted to test the evolution of 

 the solar system. Now Moult on has shown l that if the solar system 

 be converted into a gaseous spheroid, so expanded as to fill Neptune's 

 orbit, and so distributed in density as to conform to the recognized 

 laws of gases, and if the whole moment of momentum now possessed 

 by the solar system be given to it, it will not have a rate of rotation 

 sufficient to detach matter from its equator, and would not acquire 

 such a rate until it had contracted well within the orbit of the 

 innermost planet. 



(7) If the method be reversed and the expanded spheroid be given 

 the successive rates of rotation necessary to develop the rings at the 

 requisite stages, the moment of momentum of the system at each ring's 

 birth should equal the existing moment of momentum of the derived 

 bodies. But Moulton's computations show that, at the stage that gave 

 birth to the Neptunian ring, the moment of momentum of the restored 

 nebula must have been more than 200 times as great as the present 

 moment of momentum; in the Jovian stage, it must have been 140 

 times as great; in the earth stage, 1800 times as great, and in the Mer- 

 curial stage, 1100 times as great. Here is not only an enormous dis- 

 crepancy, but one that varies greatly and irregularly from stage to 

 stage. This seems to show that the discrepancies cannot be due to 

 any failure of the law of density of gases to hold good, for that should 

 give a consistent systematic error. 



1 Loc. cit. 



