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Astronomical and Nautiml Collections^ 



nearly parallel to the incident rays, the reflection is as regu- 

 lar and almost as abundant as if it had been perfectly po- 

 lished. We see, in this experiment, that the obliquity of the 

 mirror produces the same efiect as a diminution of its rough- 

 ness would do : and it is easy to see the reason of this ; for 

 the roughnesses only alter the regularity of the refraction 

 in proportion to the differences of the routes which they 

 occasion : and it is easy to demonstrate geometrically that 

 these differences become the smaller as the obliquity of the 

 rays is greater. 



We may now apply to the laws of refraction the same con- 

 siderations which have served us for explaining the laws of 

 reflection. 



Let AB be the surface separating two mediums in which 

 light is not propagated with the same velocity. We may 

 still suppose the incident rays FG and ED to have proceeded 

 from a point infinitely distant, and consequently to be pa- 

 rallel to each other : and we may investigate the effects pro 

 duced by the elementary rays refracted at an infinitely great 

 distance only, in comparison with the interval GD, or other 

 quantities of the same order, in order to simplify the state 

 of the problem. Drawing GI perpendicular to the incident 

 rays, this line will show the direction of the undulation, or, 

 in other words, the corresponding motion of the undulation 

 will arrive simultaneously at G and I, and ID is the addi- 

 tional space that ED has to describe, in order to arrive at the 



