170 Astronomical and JVautical Collections. 



different inclinations, and so become further separated as they 

 proceed. But without entering into the details of experi- 

 ments, which establish the laws of double refraction, it will 

 be sufficient to explain the principal results to which they 

 have led. 



It is remarkable, in the first place, that, when the incident 

 rays are perpendicular to the surface of the crystal, the de- 

 viation of the extraordinary pencil always takes place in the 

 plane of the principal section ; and in the next place, that 

 this deviation vanishes whenever the pencil is either parallel 

 or perpendicular to the axis. 



It has been demonstrated by observation, that when 

 the rays are parallel to the axis they not only follow the 

 same direction, but pass through the crystal with the same 

 velocity ; and it is when they are perpendicular to the axis 

 that their velocities differ the most^ although they follow the 

 same path. The velocity of the propagation of the ordinary 

 rays is the same in all directions : and for this reason they are 

 subject to the ordinary laws of refraction. The velocity of 

 the extraordinary rays is different according to the angle 

 which they make with the axis^ and this velocity is deter- 

 mined, in the system of undulation as well as in that of emana-» 

 tion, from the flexure which they undergo at their admission 

 or emersion in oblique directions, which enables us to find the 

 proportion of the sines of incidence and refraction. The ex- 

 periments of Huygens, of Dr. Wollaston, and of Malus, on 

 the carbonate of lime, and the numerous observations of Mr. 

 Biot, on rock crystal, in which the angular measures of dou- 

 ble refraction have been carried to the greatest possible pre- 

 cision, demonstrate that the difference of the squares of the 

 velocities of propagation of the ordinary and extraordinary 

 rays is proportional to the square of the sine of the angle 

 made by the extraordinary ray with the axis, if we compute 

 the velocities according to the doctrine of emanation, as the 

 celebrated author of the M^canique Celeste has done : and 

 in the theory of undulations, this same ratio is observed in 

 the reciprocals of the squares of the velocities ; for the velo- 

 cities are always reciprocally related in the two systems* 

 This important law, the discovery of which is due to the 



