If the primary wave be represented by = e-ikx the component rotations in the secondary wave are '1'3= P (- AN y) N r2 ' cwi= r x D y N 'y)' lw2=P (- AD + 6,N z2 - x2 ' D r N r2 where ik3T e-**ikr** _ P - 4 r The expression for the resultant rotation in the general case would be rather complicated, and is not needed for our purpose.

Integrating by parts in (II), we get J e = **ikr** d7 pc-11 / d (e r - ay= rJ Z d y - r / 1 dY, in which the integrated terms at the limits vanish, Z being finite only within the region T.

Dr r In like manner we find TZ x d e **ikr** 2 - 471b 2 r dr From (to), (13), (24) we see that, as might have been expected, the rotation at any point is about an axis perpendicular both to the direction of the force and to the line joining the point to the source of disturbance.

If the resultant rotation be n, we have TZ iJ (x 2 -{-y 2) de **ikr** TZsin4 d e **ikr** 2 r ' dr (r !