SECT, xxxvi.] NUMBER OF COMETS. 411 



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 perihelion 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 con- 

 sidered 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 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 de- 

 pends 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. 222). 



The celestial bodies might move in any one of these four 

 curves by the law of gravitation : but, as one particular ve- 

 locity is necessary to produce either circular or parabolic 



