138 Cataclysmic Motion [CH. vi 



The final result of the dynamical motion appears in every case to be 

 fission into detached masses, although a rigorous mathematical proof of this 

 has not been obtained. In the Tidal Problem any finite number of detached 

 masses may result (cf. fig. 23, p. 127); in the Rotational Problem the mass 

 appears to divide into two bodies of unequal size (cf. figures on p. 116); in 

 the Double-star Problem the mass breaks up into a very great number of 

 small masses. 



Hence it appears highly probable that tidal-action may produce systems 

 such as are seen in our own solar system and in the systems of Jupiter, 

 Saturn, etc.; that increasing rotation may produce systems such as are seen 

 in ordinary binary stars ; and that the close approach of two stars revolving 

 about one another may produce systems such as Saturn's rings and possibly 

 the asteroids also. We shall investigate these conjectures more fully in sub- 

 sequent chapters ; before doing so we attempt to gain some knowledge of the 

 motion of compressible and non-homogeneous masses. 



