272 THE OCEAN. [Book X. 



tend to carry it) decrease as the cube of the distance 

 increases (Proposition IV.) ; so that it must, sooner 

 or later, be brought to rest between the conflicting 

 forces. 



But, if a third revolving force exist, the equi- 

 librium must be destroyed ; because, whilst receding 

 along the tangent, the body must be inclined by that 

 third force towards the direction of one or other of 

 the equal forces, and thus be caused to revolve with 

 one or other of those centres of rotation. 



2. If the equal action of the equal forces alluded 

 to in Section 1 be in opposite directions, then the 

 body under their action can neither advance nor 

 recede, for the forces of astral gravitation, as well as 

 the direct forces, neutralise each other. 



But the action of a third force must incline the 

 body towards one or other of the two equal forces ; 

 and by that force it will then be revolved, increasing 

 unequally its distance from both centres as the 

 velocity of its motion is increased by the gradually 

 decreasing opposition of the revolving forces. 



3. Let us now suppose the revolving forces of 

 Section 1 to be unequal, then the body lying between 

 the two centres of rotation tending to carry it in the 

 same direction is accelerated, and thus carried farther 

 from both centres, until, as it inclines more and more 

 in the direction of the primary force, the conjoint 

 action ceases and becomes opposing ; and then, as the 

 motion becomes retarded, it approaches its centre of 



