On the Laws of the Double Refraction of Quartz. 65 



mulse (4), that s is the velocity of propagation for a wave whose 

 length is /, and that each vibrating molecule describes a little 

 ellipse whose semiaxes p and q are parallel to the directions of x 

 and y. But the number k, expressing the ratio of the semiaxes, 

 has two values, one of which is the negative reciprocal of the 

 other, as appears by equation (8) ; and each value of k has a cor- 

 responding value of s determined by equation (5) or (6) . Hence 

 there will be two waves elliptically polarized, and moving with 

 different velocities, the ratio of the axes being the same in both 

 ellipses ; but the greater axis of the one will coincide with the 

 less axis of the other. The difference of sign in the two values 

 of k shows that if the vibration be from left to right in one wave, 

 it will be from right to left in the other. These laws were dis- 

 covered by Mr. Airy. 



The law by which the ellipticity of the vibrations depends on 

 the inclination 0, and on the colour of the light, is contained in 

 equation (8) . The value of the constant C will be determined 

 presently. In the mean time we may observe, that C denotes a 

 line, whose length is very small, compared with the length of a 

 wave. 



When < = 0, the light passes along the axis of the crystal. 

 In this case we have k 2 = 1, and k = 1 ; which shows that there 

 are two rays, circularly polarized in opposite directions. The 

 value of s for each ray may be had from equation (5) or (6), by 

 putting + 1 and - 1 successively for k. Calling these values s' 

 and s", we find 



(10) 



Suppose a plate of quartz to have two parallel faces perpen- 

 dicular to the axis, and conceive a ray of light, polarized in a 

 given plane, to fall perpendicularly on it. The incident rectilinear 

 vibration may be resolved into two opposite circular vibrations, 



