208^* Astrotiomical and Nautical Collections y 



a very acute angle with each other, so that the breadth of 

 the reflecting space continually diminishes as it approaches 

 the angular point. If we place the mirror at a sufficient 

 distance, and receive the reflected light on a white card, and 

 then examine it with a magnifier, we shall remark that the 

 pencil reflected by the part near the angle is much broader 

 than that which comes from the remoter part, and that con- 

 sequently the divergence of the reflected rays is so much the 

 greater, as the reflecting space is narrower. 



This manner of considering the nature of reflection not 

 only explains why the rays are not subjected, in their pro- 

 gress, to the ordinary law of the equality of the angles of 

 incidence and reflection, when the surface is narrow or dis- 

 continuous, but it even furnishes the means of computing 

 their comparative intensities in their new directions. It 

 has also the advantage of giving a clear and precise idea 

 of that which constitutes a specular polish. We must not 

 consider the surface of the best polished mirror as a perfect 

 plane : it is evident, on the contrary, as Newton has already 

 remarked, even from the mechanical process of polishing, 

 that it must be roughened by an infinity of little projections; 

 for the fine powder, which is employed for this purpose^ can 

 only scratch it in every direction, and it is only the extreme 

 fineness of these scratches that renders them imperceptible. 

 But what is the degree of fineness that they must possess, in 

 order to produce a regular reflection ? This may easily be 

 inferred from the explanation that has been given of the ordi- 

 nary law of reflection. For if the points G and G'^ instead 

 of being situated exactly in the mathematical plane ADB, 

 are a little above or below this plane, there will arise, in the 

 path of the rays G^ and G'k\ a small difl'erence, which will 

 lessen their total discordance with the ray D/ ; and in the 

 particular case of a perpendicular incidence, for example, this 

 difference would be twice the projection of the points G and 

 G' above the plane ADB : if, therefore, this difference were 

 the hundredth part of the breadth of aluminous undulation, 

 the diflerence in the routes, which it would occasion, would 

 be the fiftieth of an undulation : now so small an alteration 

 from the complete discordance of the elementary rays, would 



