Astronomical and Nmitical Collections, 207 



G'G", and so forth, being equal to each other, the quantity 

 of rays which they reflect is the same : we may, therefore, 

 consider each pencil of elementary rays reflected in this di- 

 rection by any interval, DG', as destroyed by the half, in in- 

 tensity, of the rays of the preceding pencil, and by the half of 

 the following pencil. If the surface is limited, and includes 

 an even number of these intervals, the two remaining halves 

 of the extreme pencils will be completely at variance when 

 they meet, and will destroy each other at this point, so that 

 no reflected light will be visible in this direction ; but if the 

 number of intervals is odd, the light reflected in this direc- 

 tion will be as little extinguished as possible, the remaining 

 halves of the extreme pencils remaining in perfect agreement 

 with each other. It must, however, be remarked, that in this 

 case, the light diffracted, in the direction G/c, will be much 

 weaker than that which has been reflected in the direction 

 GK, since all the rays proceeding from the surface, and unit- 

 ing in the point of concourse, have described equal routes, and 

 co-operate in their effects. All the consequences of this theory 

 are confirmed by experiment. To give an idea of the extreme 

 rapidity with which the light must be diminished in propor- 

 tion as the direction GK deviates from that of the regular 

 reflection, it may be added, that even when we can reckon 

 on the surface of the mirror only five intervals such as GD, 

 which give differences of half an undulation between their 

 extreme rays, the intensity of the light refracted in the di- 

 rection Gk is only, according to the theory, J^r ^^ ^^^^ of 

 the light regularly reflected ; and when the mirror is of a 

 moderate breadth, it may easily be understood how very near 

 the direction of G^ must be to that of GK, in order that it 

 may contain but five intervals such as GD, or that there may 

 be but five semiundulations difference in the paths of the rays 

 proceeding from the two extremities of the mirror. 



It is easy to verify the consequences of this theory by throw- 

 ing, in a darkened room, the rays proceeding from a luminous 

 point on a metallic mirror, or a glass blackened at the back, 

 of which the upper surface is covered with a coat of very 

 opaque black, with the exception of a long and very narrow 

 surface, comprehended between two right lines, which make 



