98 NOMOS. 



and thus the curve of orbital motion will be more and 

 more bent until at last projection and attraction 

 begin to operate in the same direction. Up to this 

 time the orbital motion had been continually retarded 

 by the centripetal force; now the case is altered, 

 and the motion is progressively accelerated by the 

 increase of centripetal force which arises from the 

 diminished distance from the sun, until the superadded 

 velocity is sufficient to overcome the central attraction, 

 and carry the planet in the same direction and with 

 the same velocity as when it began to move. If, on 

 the other hand, the original projection be not suffi- 

 cient to counterbalance the centripetal force, and 

 maintain a purely circular orbit, the planet will at 

 once begin to fall towards the sun, and this it will 

 continue to do with continually increasing velocity 

 until the superadded motion, arising from the increas- 

 ing gravitation as the distance diminishes, is sufficient 

 to overbalance the centripetal attraction and carry it 

 in an outward direction. And then, as in the former 

 instance, the centripetal force will begin to drag upon 

 the planet, and retard its motion, until, regaining its 

 former mastery, the planet is compelled to travel in 

 the same direction and with the same velocity as when 

 it began to move. The degree of orbital eccentricity 

 must of course be proportionate to the disproportion 

 which may exist between the motion of projection and 

 the attractive force, and if this disproportion exceed 

 a certain bound there may be no proper orbit at all, 

 and, instead of moving in orbits of various eccentricity, 

 the planet might imitate some of the comets, and 

 describe hyperbolic or parabolic curves. 



