1910.] 



RESEARCHES IN COSMICAL EVOLUTION. 



213 



lar shrinkage of the surface of zero relative velocity. Accordingly 

 the particle drops down nearer and nearer these centers, and the 

 surface finally becomes closed, leaving it no longer free to move 

 about both bodies in the hour-glass shaped space, as formerly, but 



Fig. I. Curves of Zero Velocity (Darwin). This diagram illustrates the 

 hour-glass shaped space through which the particle may move and drop 

 down nearer the sun or planet, till it becomes captured by one of the 

 larger bodies. 



restricted to the sphere of influence controlled by the sun or planet 

 individually, as the case may be. The particle which once revolved 

 about both the sun and planet can no longer do so, but becomes an 

 inferior planet (satellite of the sun) or a satellite of the planet. 



It is shown that the mean distance of the planet decreases as 

 well as that of the satellite, but that the action of the resisting 

 medium is relatively more efifective on the satellite than on the planet 

 in the inverse ratio of their radii, and therefore the planet ap- 

 proaches the sun very slowly and the satellite very rapidly. Accord- 



