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 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 z = 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 



(9) 



*'" = 2 + 27T , s" = a 1 + (10) 



I \ d II 



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, 



