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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 256


256    Wisconsin Academy of Sciences, Arts, and Letters.
  Its vibrations are in the positive or the negative direction of rota-
tion in the plane of (x, y)! according as n is positive or negative.
  The light is propagated in the positive or the negative direction
of the axis of z, according as n and q are of the same or of oppo-
site signs.
  In all media n varies when q varies, and dnl is always of the"
                                            dq
                n
same sign with -.
                q
  Hence, if for a given numerical value of n, the value of -
is greater when n is positive than when n is negative, it follows
that for a given value of q, given both in magnitude and sign, the
positive value of n will be greater than the negative value.
  Now this is what is observed in a diamagnetic medium, acted
on by a magnetic force, r, in the direction of z. Of the two cir-
cularly-polarized rays of a given period, that is accelerated of
which the direction of rotation in the plane of (x, y) is positive.
Hence, of two circularly polarized rays, both left-handed, whose
wave-length within the medium is the same, that has the shortest
period whose direction of rotation in the plane of (x, y) is positive,
that is, the ray which is propagated in the positive direction of z
from south to north. We have, therefore, to account for the fact
that when in the equations of the system q and r are given, two
values of n will satisfy the equations, one- positive and the other
negative, the positive value being numerically greater than the
negative.
  We may obtain the equations of motion from a consideration of
the potential and kinetic energies of the medium. The potential
energy, V; of the system, depends on its configuration, that is, on
the relative position of its parts. In so far as it depends on the
disturbance due to circularly-polarized light, it must be a a func-
tion of r, the amplitude, and q, the coefficient of torsion, only. It
may be different for positive and negative values of q of equal
numerical value, and it probably is so in the case of media, which
of themselves rotate the plane of polarization.
  The kinetic energy, fJ of the system, is a homogeneous function
of the second degree of the velocities of the system, the coefficients
of the different terms being functions of the coordinates.


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