their several impulses, during every cornpleat revolution. 

 The power of gravitation is uniformly gaining on that of 

 projection, from the higher point of the ellipsis to the 

 lower. Now (not to ask how the projectile force reco- 

 vers itself, but supposing it had this property) I ask, by 

 what law does gravitation remit the strength it has gained, 

 in bringing the orb from the higher point to the lower, 

 and at that point allow projection to recover the force it 

 Lad lost, in order to carry it back to the higher point ? 

 In like manner seeing projection has been gaining on 

 gravitation, all the way to that point, how comes it all at 

 once to lose its superior force there ? And how comes 

 gravitation immediately to preponderate, in order to 

 bring the orb to the lower point again ] 



It cannot be said, that the increased velocity, which 

 brings a planet to the lower, contributes to carry it back 

 to the higher point. For Unit increased velocity was not 

 the effect of projection, but of gravitation. Therefore 

 the orb can never get outward again, unless at that point, 

 gravitation all at once weakens its pull of the planet 

 inwards. 



There is one circumstance more, which mathemati- 

 cians ought to consider well : namely,, that no figure 

 (circle or ellipsis) can be described by gravitation and 

 projection round lh<* centre of gravity, where the centre 

 of gravity shall not be found in the centre of the figure.. 

 But this is contrary to all astronomical observation upon 

 the motion of the planets, which determines their centre 

 of gravity to be always in one of the foci of their ellipti- 

 cal orbits. 



Yet farther. In order to move any body in a circle, 

 the moving powers must be equal, or nearly so. Now 

 the proportion ef the moving powers upon one body to 

 each other, can only be determined by the velocity of 

 the respective motions. Ii;deed, the quantity of motion 

 in different bodies must be determined by the quantity 

 of matter moving and velocities taken togelrier. But in 

 one and thesume body it may be determined solely by 

 the velocity of its motions. 



Equal powers then- can only be determined by the- 



