382 ORBITS OF COMETS. SECT. XXXV. 



because they are invisible when as distant as the orbit of Saturn : 

 on that account there is not one on record whose perihelion is 

 situate beyond the orbit of Jupiter. Indeed, the comet of 1756, 

 after its last appearance, remained five whole years within the 

 ellipse described by Saturn without being once seen. More than 

 a hundred and forty comets have appeared within the earth's 

 orbit during the last century that have not again been seen. If 

 a thousand years be allowed as the average period of each, it may 

 be computed, by the theory of probabilities, that the whole 

 number which range within the earth's orbit must be 1400 ; but, 

 Uranus being about nineteen times more distant, there may be 

 no less than 11,200,000 comets that come within the orbit of 

 Uranus. M. Arago makes a different estimate ; he considers that, 

 as thirty comets are known to have their perihelion distance 

 within the orbit of Mercury, if it be assumed that comets are 

 uniformly distributed in space, the number having their perihe- 

 lion within the orbit of Uranus must be to thirty as the cube of 

 the radius of the orbit of Uranus to the cube of the radius of the 

 orbit of Mercury, which makes the number of comets amount to 

 3,529,470. But that number may be doubled, if it be considered 

 that, in consequence of daylight, fogs, and great southern decli- 

 nation, one comet out of two must be hid from us. According 

 to M. Arago, more than seven millions of comets come within 

 the orbit of Uranus. 



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 projectile to the 

 central force is exactly that of 1 to the square root of 2, the 

 motion is parabolic ; any ratio between 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. 229). 



The celestial bodies might move in any one of these four curves 

 by the law of gravitation : but, as one particular 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 



