250 Wisconsin Academy of Sciences, Arts, and Letters. 



excess of that towards a' carries towards a' during the first part of 

 the virtual motion along ah, and towards V during the part from d 

 to h] that is, on account of the shorter time required to complete 

 an oscillation in the direction from a to h\ around the circle, than 

 in the opposite direction, there is an acceleration of phase in that 

 direction. Hence, as long as the tendency to increased rapidity of 

 one component over that of the other continues, so long will there 

 be a change in the position of the line ah. 



The application of these principles to the rotation of the plane of 

 polarization as it occurs in quartz, will be clearly shown by the 

 following extract and diagram, taken from Prest. Barnard's excel- 

 lent "Lectures on the Undulatory Theory of Light," Smithsonian 

 Annual Eeport for 1862. 



After a general discussion of circular and elliptical polarization 

 by reflection, Prest. Barnard sQ.y?<: 



" We are now perhaps prepared to understand the reason of the 

 rotation of the plane of polarization of a ray transmitted along the 

 axis of a crystal of quartz. We have seen that Fresnel, by an in- 

 genious combination of prisms, succeeded in demonstrating the 

 existence within the crystal of two circularly polarized rays, gyrat- 

 ing in opposite directions. And we have 

 seen that the resultant effect of two oppo- 

 site gyrations, is to produce a movement 

 in a plane. The gyratory movements 

 within the crystal are then not actual but 

 virtual — in other words, there are forces 

 constantly tending to produce these gyra- 

 tions, which hold each other in equilihrio, 

 or at least nearly so. We must consider 

 these forces as successively traversing 

 all azimuths within the length of each un- 

 dulation. If the wave were of the same 

 length in both gyrations, the forces being 

 presumed equal, the molecular move- 

 ment would be constantly rectilinear, and 

 the plane of polarization would not 

 change. But, as the plane does in fact change, we are led to infer 



Fig. 16. 



