SECT. XXXV. ORBITS OF COMETS. 383 



infallibly change the ratio of the forces, and cause them to move 

 in ellipses in the first case, and hyperbolas in the other-. On the 

 contrary, since every ratio between equality and that of 1 to the 

 square root of 2 will produce elliptical motion, it is found in the 

 solar system in all its varieties, from that which is nearly circular 

 to such as borders on the parabolic from excessive ellipticity. On 

 this depends the stability of the system ; the mutual disturbances 

 only cause the orbits to become more or less excentric without 

 changing their nature. 



For the same reason the bodies of the solar system might have 

 moved in an infinite variety of hyperbolas, since any ratio of the 

 forces, greater than that which causes parabolic motion, will 

 make a body move in one of these curves. Hyperbolic motion is 

 however very rare ; only two comets appear to move in orbits of 

 that nature, those of 1771 and 1824 ; probably all such comets 

 have already come to their perihelia, and consequently will never 

 return. 



The ratio of the forces which fixed the nature of the celestial 

 orbits is thus easily explained ; but the circumstances which 

 determined these ratios, which caused some bodies to move nearly 

 in circles and others to wander towards the limits of the solar 

 attraction, and which made all the heavenly bodies to rotate and 

 revolve in the same direction, must have had their origin in the 

 primeval state of things ; but as it pleases the Supreme Intelli- 

 gence to employ gravitation alone in the maintenance of this fair 

 system, it may be presumed to have presided at its creation. 



