SECT. XXXV. LIGHT OF COMETS. 381 



luminous surface consists of an infinite number of luminous 

 points, it is clear that, the greater the extent of surface, the more 

 intense will be the light ; whence it may be concluded that the 

 illuminating power of such a surface is proportional to its extent, 

 and decreases inversely as the square of the distance. Notwith- 

 standing this, a self-luminous surface, plane or curved, viewed 

 through a hole in a plate of metal, is of the same brilliancy at all 

 possible distances as long as it subtends a sensible angle, because, 

 as the distance increases, a greater portion comes into view ; and, 

 as the augmentation of surface is as the square of the diameter of 

 the part seen through the whole, it increases as the square of the 

 distance. Hence, though the number of rays from any one point 

 of the surface which pass through the hole decreases inversely as 

 the square of the distance, 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 consequence of extreme remote- 

 ness. That, however, is far from being the case comets gradu- 

 ally 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, 



