66 On the Laws of the Double Refraction of Quartz. 



which will pass through the crystal with different velocities ; and 

 which, after their emergence into air, will again compound a 

 rectilinear vibration, whose direction will make a certain angle p 

 with that of the incident vibration : so that the plane of polariza- 

 tion will appear to have been turned round through an angle 

 equal to /o, called the angle of rotation. This angle may be de- 

 termined by means of the preceding formulae. Putting for the 

 thickness of the crystalline plate, the circularly polarized wave 

 whose velocity is ' will pass through it in the time 



0_0f 7rC\ 

 7 " a \ tfl) ; 



and the wave whose velocity is s" in the time 



0_ / 7rC\ 

 s"~a\ a* I/ 



Therefore, if S be the difference of the times, we have 



But, since the velocity of propagation in air is supposed to 

 be unity, the time and the space described are represented by the 

 same quantity ; and therefore 8, which is evidently a line, de- 

 notes the distance between the fronts of the two circularly pola- 

 rized waves, when they emerge into air. The waves being at 

 this distance from each other, if we conceive, at the same depth 

 in each of them, a molecule performing its circular vibration, 

 and carrying a radius of its circle along with it, the two radii 

 will revolve in contrary directions, and will always cross each 

 other in a position parallel to the incident rectilinear vibration. 

 Now let two series of such waves be superposed, so as to agitate 

 every molecule by their compound effect, and it is evident that, 

 when the radius vector of one component vibration attains the 

 position just mentioned, the radius vector of the other will be se- 



parated from it by an angle equal to , where X is the length of 



