152. But if, whilst the projectile force carries the Planet from _B_ to _b_, the Sun’s attraction (which constitutes the Planet’s gravitation) should bring it down from _B_ to I, the gravitating power would then be too strong for the projectile force; and would cause the Planet to describe the curve _BC_. When the Planet comes to _C_, the gravitating power (which always increases as the square of the distance from the Sun _S_ diminishes) will be yet stronger for the projectile force; and by conspiring in some degree therewith, will accelerate the Planet’s motion all the way from _C_ to _K_; causing it to describe the arcs _BC_, _CD_, _DE_, _EF_, &c. all in equal times. Having it’s motion thus accelerated, it gains so much centrifugal force, or tendency to fly off at _K_ in the line _Kk_, as overcomes the Sun’s attraction: and the centrifugal force being too great to allow the Planet to be brought nearer the Sun, or even to move round him in the Circle _Klmn_, &c. it goes off, and ascends in the curve _KLMN_, &c. it’s motion decreasing as gradually from _K_ to _B_ as it increased from _B_ to _K_, because the Sun’s attraction acts now against the Planet’s projectile motion just as much as it acted with it before. When the Planet has got round to _B_, it’s projectile force is as much diminished from it’s mean state about _G_ or _N_, as it was augmented at _K_; and so, the Sun’s attraction being more than sufficient to keep the Planet from going off at _B_, it describes the same Orbit over again, by virtue of the same forces or laws. [Sidenote: Fig. IV. The Planets describe equal Areas in equal times.] 153. A double projectile force will always balance a quadruple power of gravity. Let the Planet at _B_ have twice as great an impulse from thence towards _X_, as it had before: that is, in the same length of time that it was projected from _B_ to _b_, as in the last example, let it now be projected from _B_ to _c_; and it will require four times as much gravity to retain it in it’s Orbit: that is, it must fall as far as from _B_ to 4 in the time that the projectile force would carry it from _B_ to _c_; otherwise it could not describe the curve _BD_, as is evident by the Figure. But, in as much time as the Planet moves from _B_ to _C_ in the higher part of it’s Orbit, it moves from _I_ to _K_ or from _K_ to _L_ in the lower part thereof; because, from the joint action of these two forces, it must always describe equal areas in equal times, throughout it’s annual course. These Areas are represented by the triangles _BSC_, _CSD_, _DSE_, _ESF_, &c. whose contents are equal to one another, quite round the Figure. [Sidenote: A difficulty removed.]