410 THE LIGHT OF COMETS. [SECT, xxxvi. 



of the diameter of the part seen through the whole, it increases 

 as the squares of the distances. Hence, though the number 

 of rays from any one point of the surface which pass through 

 the hole decreases inversely as the squares of the distances, 

 yet, as the extent of surface which comes into view increases 

 also in that ratio, the brightness of the object is the same to 

 the eye as long as it has a sensible diameter. For example 

 Uranus is about nineteen times farther from the sun than 

 we are, so that the sun, seen from that planet, must appear 

 like a star with a diameter of a hundred seconds, and must 

 have the same brilliancy to the inhabitants that he would 

 have to us if viewed through a small circular hole having 

 a diameter of a hundred seconds. For it is obvious that 

 light comes from every point of the sun's surface to Uranus, 

 whereas a very small portion of his disc is visible through the 

 hole ; so 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 apparent diameter, it ought to be 

 visible, like the fixed stars, and should only vanish in conse- 

 quence of extreme remoteness. That, however, is far from 

 being the case comets gradually become dim as their distance 

 increases, 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 perihelia 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 



