280 THE OCEAN. [Book X 



recedes from the central force. And as the revolving 

 force of the inner one accelerates the motion of the 

 outer one round the central force, the centrifugal 

 force of astral gravitation, increasing as the square of 

 the velocity, carries the outer one farther from the 

 common centre ; whilst at the same time the revolving 

 force of the outer body retards the motion of the 

 inner one round the common centre, and the conse- 

 quent decrease of the centrifugal force of astral 

 gravitation therefore lets it fall nearer to the common 

 centre. 



Thus, as the two bodies revolve round the central 

 force, the revolution round each other is performed 

 in an elliptical, instead of the circular orbit which 

 their own undisturbed action would cause. 



5. Then, as regards the action of this central 

 force on the bodies m Section 2. In this case the 

 body whose axis lies in the plane of rotation may 

 for the present be regarded as having no axial rota- 

 tion, as we consider the one which revolves it to 

 revolve in the same plane as the central body. 



In this case the action would be the same as in 

 Section 4, except that, as there is no reciprocal revolv- 

 ing action between the two lesser bodies, the changing 

 of the form of the orbit is not the same when the 

 revolving body is inside as when it is outside the 

 greater orbit ; and therefore the orbit of the non- 

 rotating body round its primary, instead of being a 

 true ellipse, is wider when the non-rotating body is 



