412 ORBITS OF COMETS. [SECT, xxxvr. 



motion, such motions can hardly be supposed to exist in the 

 solar system, where the bodies are liable to such mutual 

 disturbances as would infallibly change the ratio of the forces, 

 .and cause them to move in ellipses in the first case, and hyper- 

 bolas 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 eccentric with- 

 out 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 celes- 

 tial 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 Intelligence to employ gravitation alone in the 

 maintenance of this fair system, it may be presumed to have 

 presided at its creation. 



