Overhead cables and electric fields

I have been wondering for a while what the horizontal pieces with the curved ends are that sit beneath the stack of insulators. I think I might have worked it out. They seem to be connected to the wire suspension point so they will have the same potential (voltage) as the wire. If they were not there, there would be a single suspension point at that potential beneath the insulators. Single points concentrate the electric field lines into a smaller space. Electric field lines are like contours. The closer they are the stronger the field. Air can only take a certain field strength before it breaks down and conducts by sparks. By including this bar, the field lines are spread out making it less likely to spark. That's my theory. It looks different with horizontal suspension:

I'm not sure why there is only half a bar this time.