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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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