SECT. XXXVI. NUMBER OF COMETS. 359 



that extent of surface exactly compensates distance. 

 Since, then, the visibility of a self-luminous object does 

 not depend upon the angle it subtends as long as it is 

 of sensible magnitude, if a comet shines by its own light, 

 it should retain its brilliancy as long as its diameter is of 

 a sensible magnitude ; and even after it has lost an ap- 

 parent diameter, it ought to be visible, like the fixed 

 stars, and should only vanish in consequence of extreme 

 remoteness. That, however, is far from being the case 

 comets gradually become dim as their distance in- 

 creases, and vanish merely from loss of light, while 

 they still retain a sensible diameter, which is proved by 

 observations made the evening before they disappear. 

 It may therefore be concluded, that comets shine by 

 reflecting the sun's light. The most brilliant comets 

 have hitherto ceased to be visible when about five times 

 as far from the sun as we are. Most of the comets 

 that have been visible from the earth have their peri- 

 helia within the orbit of Mars, 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 known extent of our sys- 

 tem. M. Arago makes a different estimate : he con- 

 siders 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 * e doubled, 



