DOUBLE REFRACTION. Ill 



duced to meet these surfaces, and tangent planes be drawn at the 

 points of meeting, the line of intersection of these planes will be on 

 the separating surface of the two media.* Hence the position of 

 the refracted ray is determined when that of the incident ray is 

 known ; and the construction thus supplied for its determination 

 is obviously the generalization of the construction of Huygens 

 already alluded to, if only the radii- vectores be taken in the direct 

 ratio of the velocities, instead of the inverse. 



It is obvious, then, that the problem of double refraction, con- 

 sidered as a physical question, resolves itself into the determination 

 of the law of velocities. Newton showed that the constant ratio 

 of the velocities in ordinary media, and therefore the law of the 

 sines, could be explained on the supposition that the luminous 

 molecules are solicited by attracting forces emanating from the 

 molecules of the refracting body, and sensible only at very small 

 distances. The phenomenon of extraordinary refraction, in like 

 manner, was ascribed by Laplace to the operation of similar forces 

 emanating from the molecules of the crystal, but modified by the 

 form of these molecules and those of light, and by the manner in 

 which they are presented to each other. No attempt, however, 

 has been made in the theory of emission to advance beyond the 

 point at which Newton arrived, and to deduce the velocity of the 

 extraordinary ray in crystallized media from any assumed consti- 

 tution of the molecular forces ;t and, indeed, when the condition 

 of polarity is to be superadded to the laws of such forces, the theory 

 seems embarrassed in inextricable difficulties. The refraction which 

 a polarized ray undergoes in a crystal depends upon its plane of 

 polarization ; and, by a simple change of that plane, the refracted 

 ray may be converted from an extraordinary to an ordinary ray. 

 The extraordinary force then, it appears from the phenomena, 

 exerts no effect upon a ray polarized parallel to the principal 

 plane. Its effect is greatest upon a ray polarized in the perpen- 

 dicular plane ; and it must be supposed to act in every intermediate 



* Mem. Inst. 1816. 



t Fresncl states, in the commencement of his memoir on double refraction, that 

 Laplace had derived the velocity of the extraordinary ray, in uniaxal crystals, from 

 the hypothesis of a resultant force acting in a direction perpendicular to the optic axis, 

 and varying as the square of the sine of the angle which the ray makes with that line. 

 I have not been able to discover, in any of Laplace's writings, the discussion thus 

 adverted to. 



