AstfonoJnical and Nautical Collections. 205' 



different intensities. It would, no doubt, be difficult to deter- 

 mine the law of the variation of their intensities in different 

 directions about these points : but happily there is no occasion 

 for such a determination ; for, whatever the law might be, 

 it is evident, that the rays passing from the two points in 

 parallel directions would be similarly affected by it, and must 

 possess the same intensity and the same elementary direction 

 of oscillation : so that this principle is sufficient to enable us 

 to judge of the direction in which the resulting undulations 

 can be propagated. In fact, we may consider the reflected 

 undulation at a distance from AB infinitely great, in com- 

 parison with GD, and other intervals of the same order : and 

 supposing GK and DL to be two elementary rays that have 

 been reflected, and that are proceeding to contribute to 

 the formation of an elementary point of this distant undula- 

 tion, and therefore parallel ; and the angle KGB being equal 

 to EDA ; it is clear that the elementary motions transmitted 

 in the lines GK and DL will agree perfectly with each other: 

 for on account of the equality of the angles, if we draw DC 

 perpendicular to GK, the two triangles GDC and DIG will 

 be equal, and consequently GC will be equal to DI. But 

 DI is the portion of the path of the incident ray ED, which 

 it has described in its passage to the surface, after the de- 

 scription of EG by its collateral ray, and (X is the portion 

 of the path of the ray reflected at G, which it has to describe 

 beyond that which is reflected at D, in order to arrive at the 

 point of their meeting : consequently when they meet, they 

 will both have described the same space, and will perform 

 their motions in perfect agreement. 



But this would be no longer true, if the direction of the 

 reflected rays were Gk and D^, which are supposed also to 

 meet in a point infinitely distant, but not to make an angle 

 with the surface equal to EDA ; for then the interval Gc, 

 comprehended between the point G and the end of the per- 

 pendicular D(?, being no longer equal to ID, the paths de- 

 scribed by the rays in order that they may arrive at the point 

 of meeting, are no longer equal, and their oscillations at this 

 point must be more or less discordant ; now we may always 

 take G at such a distance from D, that the drfl^erence of GC 



