72 THE OCEAN. [Book III. 



(supposing it to be free from the action of foreign 

 forces of gravitation), and that it may be so increased 

 as to carry the body quite round the earth, or an 

 indefinite number of times round the earth, even 

 then, that the body can twice return exactly to the 

 point V, fi:om which it started, or that it must not 

 necessarily, sooner or later, in the course of time 

 come to the surface of the earth just as certainly as 

 that projected from vto d, — is not shown. And, in 

 fact, it is certain that no increase in the amount of the 

 projecting force can prevent the body firom being 

 gradually more and more deflected from the horizontal 

 line, untU it at length be brought to the surface of the 

 earth. For the force with which the body is projected 

 in the horizontal line is supposed to resist the force 

 with which the earth draws the body towards its sur- 

 face ; but in resisting this tendency of the earth to 

 draw the body towards it, a greater or lesser amount 

 of force is necessarily spent. And as the force with 

 which the earth draws the body towards it is con- 

 tinuous, which the projecting force is not, this latter 

 must at length be spent by the constant resistance of 

 the former ; and the body, therefore, must at length 

 be brought to rest on the surface of the earth, just as 

 certainly, and for the same reasons, as in the case of 

 the ball rolled along the ground. In both cases a 

 certain amount of force is expended to set bodies in 

 motion ; and as the force is not continuous in its 

 action, it is at length spent by the constant resistance 



