i<30 ASTRONOMY. 



would then be too strong for the projectile force, 

 and would cause the planet to describe the curve 

 B C. When the planet comes to C, the gravitat- 

 ing 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 con- 

 spiring in some degree therewith, will accelerate 

 the planet's motion all the w r ay from C to K, caus- 

 ing it to describe the arcs B C, C D, D E, E F, &c. 

 all in equal times. 



Having its motion thus accelerated, it thereby 

 acquires so much centrifugal force, or tendency to 

 fly off at K, in the line K k, as overcomes the sun's 

 attraction ; and the centrifugal force being too 

 great to allow the planet to be brought nearer to 

 the sun, or even to move round him in the circle 

 klmn, &c. it goes off, and ascends in the curve 

 K L M N, &c. its motion decreasing as gradually 

 from K to B, as it increased from B to K, because 

 the sun's attraction now acts against the planet's 

 projectile motion, just as much as it acted with it 

 before. 



When the planet has got round to B, its pro- 

 jectile force is as much diminished from its mean 

 state 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 powers. 



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 to- 

 wards 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 



