206 Astronomical and Nautical Collections. 



and ID may be equal to a semiundulation ; which will esta- 

 blish a complete discordance, at the point of concourse, be- 

 tween the oscillations reflected along the lines G^ and Dl ; 

 and as they are besides of [equal] intensities, they will mu- 

 tually destroy each other ; and there can consequently be no 

 light reflected in that direction. 



So true is it that the elementary ray Dl is neutralised in 

 this case, by that which comes from the point G, that if we 

 suppress this last, and the other rays which are sufficiently 

 near to co-operate with it in counteracting Dl, we give, or 

 rather we restore to the latter, the faculty of appearing in 

 its place. The different elementary rays, reflected at D, are 

 so much the more capable of diverging, as the extent of the 

 reflective surface is the more confined on each side of this 

 point ; for the elementary ray G'k' proceeding from a point 

 G situated at the same distance from D as the point G, coun- 

 teracts the oscillations of D/at the point of meeting, as well 

 as the ray G^ ; and the general mode of representing these 

 mutual destructions of the elementary ra3^s is to consider each 

 intermediate ray Dlas destroyed b}^ the half, in intensity, of 

 the ray Gk, together with half of G'^' : and then the remain- 

 ing halves of these two rays by the halves of the next on each 

 side, and so forth. 



if we divide in this manner the surface of the mirror into a 

 series of parts DG', G'G', and so forth, equal to GD ; the 

 elementary rays reflected at the points G, D, G', G", all directed 

 to the same point of concourse at an infinite distance, and 

 consequently parallel to each other, will differ by pairs half 

 an undulation in their route : thus, for example, the ray Gy^ 

 will be found half an undulation in advance of the ray D/, and 

 this the same distance in advance of the ray G'^', and so forth : 

 for the same reason, the ray proceeding from the middle of 

 the line GD will be completely at variance with the ray from 

 the middle of DG', and a similar discordance will take place 

 between the rays reflected from all the other corresponding 

 points of GD and DG' : in the same manner, all the rays re- 

 flected at the different points of DG' will be completely at 

 variance with these which are reflected at the corresponding 

 points of G'G", and so forth : now the intervals GD, DG', 



