24 M. Arago on the Light of Comets. 



all imaginable distances, so long as it subtends a sensible angle ? 

 A few brief reflections will cause all that at first appears strange 

 in this result speedily to vanish. 



When we set about comparing not illuminating power s, but 

 luminous intensities, it is necessary to choose in the two bo- 

 dies under our view, two portions of the same angular extent 

 — two circular spaces seen under the same angle — under the 

 angle of a minute, for example; and to discover, whilst simul- 

 taneously examining them, which of the two seems the most 

 brilliant. Suppose there reach the eye, through openings of 

 the thousandth part of a square yard diameter, rays, coming 

 from two plane surfaces A and B, which are found, at these 

 openings, of equal intensities ; then this equality will not be al- 

 tered if, the surface B being retained in its place, we shall 

 transport the surface A 2 times, 3 times, . . . times, 100 times, 

 further from us, provided that, at all these distances, the cor- 

 responding opening shall be completely filled with rays. 



In fact, it is true that, in proportion as the surface A is with- 

 drawn, each of its points transmits, into the circular opening which 

 the observer employs, a progressively decreasing number of rays ; 

 whilst, on the other hand, the extent of the surface which the 

 eye discovers, through the same opening, is so much more ex- 

 tensive ; it embraces a number of luminous points so much the 

 more considerable as the increase of distances is the greater. We 

 must now examine if these two contrary results compensate the 

 one for the other. 



Every one will comprehend, that the diverging lines proceed- 

 ing from the eye, and striking the two extremities, of different 

 diameters, of the circular opening through which we look upon 

 the plane A, will embrace upon the plane, rectilinear intervals 

 equal amongst themselves, and the extent of which will be pro- 

 portional to the distance which separates it from the observer. 

 Thus, at the distances 1, % 3, ... , 100, the real length of the 

 diameters of the circles which we may discover upon the surface 

 A will be in the ratio of the numbers 1, 2, 3, . . ., 100; and 

 geometry teaches us that the surfaces of circles vary in the ratio 

 of the squares of their diameters. The number of the luminous 

 points of the surface, therefore, which we shall perceive through 



