360 ORBITS OF COMETS. SECT. XXXVI. 



if it be considered that, in consequence of daylight, fogs, 

 and great southern declination, one comet out of two 

 must be hid from us. According to M. Arago, more 

 than seven millions of comets frequent the planetary 

 orbits. 



The different degrees of velocity with which the 

 planets and comets were originally propelled in space is 

 the sole cause of the diversity in the form of their orbits, 

 which depends only upon the mutual relation between 

 the projectile force and the sun's attraction. 



When the two forces are exactly equal to one another, 

 circular motion is produced ; when the ratio of the pro- 

 jectile to the central force is exactly that of 1 to the 

 square root of 2, the motion is parabolic ; any ratio be- 

 tween these two will cause a body to move in an ellipse, 

 and any ratio greater than that of 1 to the square root of 

 2 will produce hyperbolic motion (N. 222). 



The celestial bodies might move in any one of these 

 four curves by the law of gravitation ; but as one par- 

 ticular velocity is necessary to produce either circular or 

 parabolic 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 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 para- 

 bolic from excessive eUipticity. 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 com- 

 ets have already come to their perihelia, and conse- 

 quently will never return. 



