CuAP. XXI.] THE HEAVENS. 223 



and therefore, whilst vis-inertia3 keeps it in equilibrium 

 between these opposing forces, the body will neither 

 reach the new position to which the motive force tends 

 to carry it, nor remain in the old position in which the 

 remainder of the force of gravitation tends to retain 

 it. So that it must have a real motion from the old 

 position, but at the same time can never reach the 

 point to which the motive force endeavours to carry it. 

 Therefore, whilst held in equilibrium by vis- 

 inertiae, the moon has a real motion in the same 

 direction as that of the motive force, which latter is 

 its gravitation towards the nearest part of the earth's 

 surface endeavouring to carry it along with the 

 motion of that surface (Proposition II.) : but the 

 remaining force of gravitation, which is astral gravi- 

 tation, as defined in Book III., keeps it constantly 

 from reaching the point to which the motive force 

 endeavours to carry it ; and therefore gives it an 

 apparent motion over the earth's surface in the 

 opposite direction to that in which the surface 

 endeavours to carry it. 



PROPOSITION VIII. 



Theorem. — If the planets as they revolve in their orbits 

 are in equilibrium between the revolving force 

 of the sun's gravitation, tending to carry them 



