Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/439

Rh 820.] Every term of $$T$$ is of two dimensions as regards velocity. Hence the terms involving $$n$$ must involve some other velocity. This velocity cannot be $$\dot{r}$$ or $$\dot{q}$$, because, in the case we consider, $$r$$ and $$q$$ are constant. Hence it is a velocity which exists in the medium independently of that motion which constitutes light. It must also be a velocity related to $$n$$ in such a way that when it is multiplied by $$n$$ the result is a scalar quantity, for only scalar quantities can occur as terms in the value of $$T$$, which is itself scalar. Hence this velocity must be in the same direction as $$n$$, or in the opposite direction, that is, it must be an angular velocity about the axis of $$z$$.\

Again, this velocity cannot be independent of the magnetic force, for if it were related to a direction fixed in the medium, the phenomenon would be different if we turned the medium end for end, which is not the case.

We are therefore led to the conclusion that this velocity is an invariable accompaniment of the magnetic force in those media which exhibit the magnetic rotation of the plane of polarization.

821.] We have been hitherto obliged to use language which is perhaps too suggestive of the ordinary hypothesis of motion in the undulatory theory. It is easy, however, to state our result in a form free from this hypothesis.

Whatever light is, at each point of space there is something going on, whether displacement, or rotation, or something not yet imagined, but which is certainly of the nature of a vector or directed quantity, the direction of which is normal to the direction of the ray. This is completely proved by the phenomena of interference.

In the case of circularly-polarized light, the magnitude of this vector remains always the same, but its direction rotates round the direction of the ray so as to complete a revolution in the periodic time of the wave. The uncertainty which exists as to whether this vector is in the plane of polarization or perpendicular to it, does not extend to our knowledge of the direction in which it rotates in right-handed and in left-handed circularly-polarized light respectively. The direction and the angular velocity of this vector are perfectly known, though the physical nature of the vector and its absolute direction at a given instant are uncertain.

When a ray of circularly-polarized light falls on a medium under the action of magnetic force, its propagation within the medium is affected by the relation of the direction of rotation of the light to