358 LIGHT OF COMETS SECT. XXXVT. 



light has never been satisfactorily made out till now. 

 Even if the light of a comet were polarized, it Would 

 not afford a decisive test, since a body is capable of re- 

 flecting light though it shines by its own. M. Arago, 

 however, has with great ingenuity discovered a method 

 of ascertaining this point, independent both of phases 

 and polarization. 



Since the rays of light diverge from a luminous point, 

 they will be scattered over a greater space as the dis- 

 tance increases, so that the intensity of the light on a 

 screen two feet from the object, is four times less than 

 at the distance of one foot ; three feet from the object 

 it is nine times less, and so on, decreasing in intensity 

 as the squares of the distances increase. As a self- 

 luminous surface consists of an infinite number of lumi- 

 nous points, it is clear that the greater the extent of sur- 

 face, the more intense will be the light; whence it may 

 be concluded that the illuminating power of such a sur- 

 face is proportional to its extent, and decreases inversely 

 as the squares of the distances. Notwithstanding 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 hole, 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 ex- 

 ample 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 inhab- 

 itants that he would have to us if viewed through a 

 small circular hole having a diameter of a hundred sec- 

 onds. 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 



