Memoirs presented to the Cambridge philosophical society on the occasion of the jubilee of Sir George Gabriel Stokes, bart., Hon. LL. D., Hon. SC. D., Lucasian professor.

AND THE INFLUENCE OF A MAGNETIC FIELD ON OPTICAL PHENOMENA. 401
this may be expressed in the form
4a2(f, g', h')=- (KP1 - d2P + na3 dQ mao dR )
+ V dt V dt ' '
so that, when K1i, K2, K3 are each equal to K, the equations of propagation are reducible
to the normal form for a non-rotational medium by imparting to the coordinate axes a
velocity of rotation 2r20K -X-2(lal, mna3), which implies a coefficient of rotation of a
plane-polarized wave equal per unit distance to 27r2K-1X-2(la1, ma2, na,) where X is the
wave-length in vacuum. This is the law of rotation for wave-trains travelling in various
directions in a simply refracting medium with aeolotropic rotational quality. This law
also applies approximately to crystals such as quartz, inasmuch as the difference between
the principal refractive indices is not considerable: in quartz the vector (ai, a,, a3) must
by symmetry coincide with the axis of symmetry of the crystal: thus the coefficient of
the effective component, that normal to the wave-front, of the imposed rotation for a
wave-train that travels in a direction making an angle 0 with that axis is proportional
to cos2 0, not to cos 0 as in the magnetic case. In this case the rotational effect is
superposed on the double refraction, so that a plane-polarized wave instead of being
simply rotated will acquire varying elliptic polarization: it is however a simple problem
in kinematics* to determine the types and the velocities of the two elliptically polarized
wave-trains that will be propagated without change of form under the two influences,
each supposed slight.
It appears from this discussion that magneto-optic rotation is a phenomenon of
kinetic origin, related to the free periods of the molecules and not at all to their
mean polarization under the action of steady electric force: it is therefore entirely of
dispersional character.
Again the intrinsic optical rotation of isotropic chiral media is represented by a constitutive relation of type
f K P+ (dQ dR
f,rC2 dz dy)'
showing that the rotational term is proportional to the time-gradient of the magnetic field
this effect would therefore be entirely absent in statical circumstances, and only appears
sensibly in vibratory motion of very high frequency. In this case no physical account of the
origin of the term has been forthcoming: we have to be content with the knowledge that
the form here stated is the only one that is admissible in accordance with the principles
of dynamics.
As the rotatory power, of both types, is thus connected with the dispersion as well as
the density of the material, it is not strange that attempts, experimental and theoretical,
to obtain a simple connexion with the density alone, have not led to satisfactory results.
The existence of a definite rotational constant for each active substance hbas formed the
main experimental resource in the advance of stereochemical theory: but the present
considerations prepare us for the fact that no definite relations connecting rotational power
with constitution have been fonnd to exist,-that the quality, though definite, is so to
speak a slight and accidental one, or rather one not directly expressible in terms either of
crystalline structure or of the main constitutive relations with which chemistry can deal.
* Cf. Gouy, Joutrln. de Phys., 1885; Lefebvre, loc. cit., 1892; O. Wiener, Wied. Ann., 1888.
VOL. XVIII. 51