which completely determines the rotation at any point. For a disturbing force of given integral magnitude it is seen to be everywhere about an axis perpendicular to r and the direction of the force, and in magnitude dependent only upon the angle (φ) between these two directions and upon the distance (r).
The intensity of light is, however, more usually expressed in terms of the actual displacement in the plane of the wave. This displacement, which we may denote by ζ′, is in the plane containing z and r, and perpendicular to the latter. Its connexion with ωis expressed by ω = dζ′/dr; so that
| ζ′ = | TZ sin φ | · | e′ (at−kr) | (16), |
| 4πb² | r |
where the factor eint is restored.
Retaining only the real part of (16), we find, as the result of a local application of force equal to
DTZ cos nt (17),
the disturbance expressed by
| ζ′ = | TZ sin φ | · | cos (nt − kr) | (18). |
| 4πb² | r |
The occurrence of sin φ shows that there is no disturbance radiated in the direction of the force, a feature which might have been anticipated from considerations of symmetry.
We will now apply (18) to the investigation of a law of secondary disturbance, when a primary wave