Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/437

Rh 817.] The disturbance, being a vector, can be resolved into components parallel to $$x$$ and $$y$$, the axis of $$z$$ being parallel to the direction of the ray. Let $$\xi$$ and $$\eta$$ be these components, then, in the case of a ray of homogeneous circularly-polarized light,

In these expressions, $$r$$ denotes the magnitude of the vector, and $$\theta$$ the angle which it makes with the direction of the axis of $$x$$.

The periodic time, $$\tau$$, of the disturbance is such that

The wave-length, $$\lambda$$, of the disturbance is such that

The velocity of propagation is $$\frac{n}{q}$$.

The phase of the disturbance when $$t$$ and $$z$$ are both zero is $$\alpha$$.

The circularly-polarized light is right-handed or left-handed according as $$q$$ is negative or positive.

Its vibrations are in the positive or the negative direction of rotation 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 opposite signs.

In all media $$n$$ varies when $$q$$ varies, and $$\frac{dn}{dq}$$ is always of the same sign with $$\frac{n}{q}$$.

Hence, if for a given numerical value of $$n$$ the value of $$\frac{n}{q}$$ is greater when $$n$$ is positive than when $$n$$ is negative, it follows that for a 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, $$\gamma$$, in the direction of $$z$$. Of the two circularly-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 $$xy$$ 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