Becquerel (_Comptes rendus_, 125, p. 683) gives for r the expression e H dµ ½ --- ---- ---------, m v0 d[lambda] where [lambda] is the wave length. This is equivalent to (2) if µ is given by (1). He has shown that this expression is in good agreement with experiment. The sign of r depends on the sign of e, hence the rotation due to negative ions would be opposite to that for positive. For the great majority of substances the direction of rotation is that corresponding to the negation ion. We see from the equations that the rotation is very large for such a value of p as makes P = 0: this value corresponds to a free period of the ions, so that the rotation ought to be very large in the neighbourhood of an absorption band. This has been verified for sodium vapour by Macaluso and Corbino.[43] If plane-polarized light falls normally on a plane face of the medium containing the ions, then if the electric force in the incident wave is parallel to x and is equal to the real part of A[epsilon]^[l(pt - qz)], if the reflected beam in which the electric force is parallel to x is represented by B[epsilon]^[l(pt + qz)] and the reflected beam in which the electric force is parallel to the axis of y by C[epsilon]^[l(pt + qz)], then the conditions that the magnetic force parallel to the surface is continuous, and that the electric forces parallel to the surface in the air are continuous with Y0, X0 in the medium, give A B [iota]C ----------------- = ----------- = ---------- (q + q1) (q + q2) (q² - q1q2) q(q2 - q1) or approximately, since q1 and q2 are nearly equal, [iota]C q(q2 - q1) (µ² - 1)pH ------- = ---------- = ------------. B q² - q1² 4[pi]µne V0² Thus in transparent bodies for which µ is real, C and B differ in phase by [pi]/2, and the reflected light is elliptically polarized, the major axis of the ellipse being in the plane of polarization of the incident light, so that in this case there is no rotation, but only elliptic polarization; when there is strong absorption so that µ contains an imaginary term, C/B will contain a real part so that the reflected light will be elliptically polarized, but the major axis is no longer in the plane of polarization of the incident light; we should thus have a rotation of the plane of polarization superposed on the elliptic polarization.