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Transactions of the Wisconsin Academy of Sciences, Arts and Letters
volume IV (1876-1877)

Davies, J. E.
Report on recent progress in theoretical physics,   pp. 241-264 PDF (6.7 MB)

Page 250

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 ab, and towards 6' during the part from 0
to b; that is, on account of the shorter time required to complete
an oscillation in the direction from a' to b', 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 ab.
  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 Report for 1862.
  After a general discussion of circular and elliptical polarization
by re/1ection, Prest. Barnard says:
  "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 cirmularly polarized rays, gyrat-
        Fig. 16.      ing in opposite directions. And we have
    po X            -   seen that the resultant effect of two oppo-
             N    9    site gyrations, is to produce a movement
 A ,,'  Gall  LAB - in a plane. The gyratory movements
           I 10 6  ate  within the crystal are then not actual but
                  F 3) W   virtual- in other words, there are forces
                  F F~kXconstantly tending to produce these gyra-
                        tions, which hold each other in equilibrio,
                        or at least nearly so. We must consider
       ,l!            these forces as successively traversing
 o                      all azimuths within the length of each un-
 tc  Q     'K \         dulatibn. If the wave were of the same
                         length in both gyrations, the forces being
       -X  , ----v    wresumed 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

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