1 10 DOUBLE REFRACTION OF CRYSTALS. 



perpendicularly on a second crystal cut by a plane perpendicu- 

 lar to its axis : it is clear, ihat an infinitely small inclination of 

 the axis to the face of incidence will be sufficient to change this 

 ray into an extraordinary ray. But this inclination can pro- 

 duce but an infinitely small change in the action of the crystal, 

 and consequently in the velocity of the ray within it : this velo- 

 city, then, is that of the extraordinary ray, and consequently it 

 is equal to j- : which comes to the same as the result of Huy- 

 gens : for it is known, that the velocity of light, in common 

 transparent mediums, expresses the ratio of the sines of inci- 

 dence and refraction, its velocity in vacuo being taken as unity. 

 Reflection of The principle of least action may serve also to determine the 

 '^^^' laws of the reflection of light ; for, though the nature of the 



force, that causes light to rebound from the surfaces of bodies, 

 is unknown, it may be considered as a repulsive force, which 

 restores, in a direction contrary to that of the light, the velocity- 

 it causes it to lose; as elasticity restores to bodies in a contrary 

 direction, the velocity which it destroys. Now we know, that, 

 in this case, the principle of least action always subsists. With 

 respect to a luminous ray, whether ordinary or extraordinary, 

 reflected by the exterior surface of a body, the principle is re- 

 duced to this, that the light passes from one point to another by 

 the shortest path of all those that fall in with the surface. In 

 fact, the velocity of reflected light is the same as that of direct 

 light : and it may be laid down as a general principle, that, 

 when a ray of light, after having experienced the action of as 

 many forces as you ple-ase, returns into a vacuum, it re nines its 

 original velocity. The condition of the shortest path gives the 

 equality of the angles of reflection and incidence in a plane 

 perpendicular to the surface, as Ptolemy had already remarked. 

 It is the general law of reflection at the external surfaces of 

 bodies. 

 Reflection in But when light, on entering into a crystal, is divided into 

 J , M^*^ f^ ordinary and extraordinary rays, one portion of these rays is re- 

 tion. fleeted by the interior surface at their exit from the crystal. In 



being reflected, each ray, whether ordinary, or extraordinary, 

 divides into two others j so that a solar ray, penetrating the 

 crystal, forms by its partial reflection at the surface of emission 

 four distinct pencils, the direction of which I shall proceed to 

 determine. 



Let 



