The properties of Alfv6n waves in a vertical column of field are pointed out as a guide in treating the complicated problem of overstability. There are internal Alfv6n waves of arbitrary form propagating along the magnetic field, without disturbing the fluid outside the column. There are also surface waves which involve the fluid both inside and outside the column of field. The surface waves propagate at a speed less than the Alfv6n speed.
Convective forces couple the internal and external fluid motions. If the forces are not too strong, the identity of the modes, as internal waves or surface waves, is maintained. The surface waves are unstable and, we suggest, may contribute to some of the activity of a sunspot. We suggest that the internal Alfv6n wave modes are of more central interest for producing the basic sunspot phenomena. They represent the degenerate case, and their form is worked out in some detail. The overstable Alfv6n wave modes peak sharply near the outer edge of the field, and do not strongly disturb the fluid outside. We suggest that this effect contributes to the sharp edge of the sunspot umbra.
Recent observations by Giovanelli show intense wave activity originating inside the edge of the umbra. We tentatively identify the activity with the peak in the overstable modes within the umbra.